{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "6530e77f",
   "metadata": {
    "papermill": {
     "duration": 0.024543,
     "end_time": "2021-06-17T12:39:24.039027",
     "exception": false,
     "start_time": "2021-06-17T12:39:24.014484",
     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "# The Cookbook of Neural ODEs\n",
    "\n",
    "`torchdyn` implements out-of-the-box a variety of continuous-depth models. In this introductory tutorial, we show how we can switch between model variants with minor effort. We will touch upon the following Neural ODE variants:\n",
    "\n",
    "* **Vanilla** (depth-invariant) (same as the [torchdyn quickstart](./00_quickstart.html) tutorial)\n",
    "* **Vanilla** (depth-variant)\n",
    "* **Galerkin**\n",
    "* **Data-controlled**\n",
    "* **Stacked (piece-wise constant weights)**\n",
    "* **Stacked with discrete state transitions**\n",
    "--------------------------------------\n",
    "\n",
    "For more advanced models check out \n",
    "\n",
    "* Multiple Shooting Layers\n",
    "* [Hamiltonian Neural Networks](./06a_hamiltonian_nn.html)\n",
    "* [Lagrangian Neural Networks](./06b_lagrangian_nn.html)\n",
    "* [Continuous Normalizing Flows](./07_continuous_normalizing_flow.html)\n",
    "* [Graph Neural ODEs](./08_graph_neural_de.html)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "599a9175",
   "metadata": {
    "papermill": {
     "duration": 1.118505,
     "end_time": "2021-06-17T12:39:25.175944",
     "exception": false,
     "start_time": "2021-06-17T12:39:24.057439",
     "status": "completed"
    },
    "tags": []
   },
   "outputs": [],
   "source": [
    "from torchdyn.core import NeuralODE\n",
    "from torchdyn.nn import DataControl, DepthCat, Augmenter, GalLinear, Fourier\n",
    "from torchdyn.datasets import *\n",
    "from torchdyn.utils import *\n",
    "\n",
    "%load_ext autoreload\n",
    "%autoreload 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "f7ecc430",
   "metadata": {
    "tags": [
     "parameters"
    ]
   },
   "outputs": [],
   "source": [
    "# quick run for automated notebook validation\n",
    "dry_run = False"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "163ca251",
   "metadata": {
    "papermill": {
     "duration": 0.018588,
     "end_time": "2021-06-17T12:39:25.218468",
     "exception": false,
     "start_time": "2021-06-17T12:39:25.199880",
     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "**Data:** we use again the moons dataset (with some added noise) simply because all the models will be effective to solve this easy binary classification problem.\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "0b51385f",
   "metadata": {
    "papermill": {
     "duration": 0.023454,
     "end_time": "2021-06-17T12:39:25.260625",
     "exception": false,
     "start_time": "2021-06-17T12:39:25.237171",
     "status": "completed"
    },
    "tags": []
   },
   "outputs": [],
   "source": [
    "d = ToyDataset()\n",
    "X, yn = d.generate(n_samples=512, dataset_type='moons', noise=.1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "1ab4ef82",
   "metadata": {
    "papermill": {
     "duration": 2.995151,
     "end_time": "2021-06-17T12:39:28.274655",
     "exception": false,
     "start_time": "2021-06-17T12:39:25.279504",
     "status": "completed"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 216x216 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "\n",
    "colors = ['orange', 'blue'] \n",
    "fig = plt.figure(figsize=(3,3))\n",
    "ax = fig.add_subplot(111)\n",
    "for i in range(len(X)):\n",
    "    ax.scatter(X[i,0], X[i,1], s=1, color=colors[yn[i].int()])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "404a1055",
   "metadata": {
    "papermill": {
     "duration": 4.507785,
     "end_time": "2021-06-17T12:39:32.805540",
     "exception": false,
     "start_time": "2021-06-17T12:39:28.297755",
     "status": "completed"
    },
    "tags": []
   },
   "outputs": [],
   "source": [
    "import torch\n",
    "import torch.utils.data as data\n",
    "device = torch.device(\"cuda:0\" if torch.cuda.is_available() else \"cpu\")\n",
    "\n",
    "X_train = torch.Tensor(X).to(device)\n",
    "y_train = torch.LongTensor(yn.long()).to(device)\n",
    "train = data.TensorDataset(X_train, y_train)\n",
    "trainloader = data.DataLoader(train, batch_size=len(X), shuffle=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "98f3dfd5",
   "metadata": {
    "papermill": {
     "duration": 0.019241,
     "end_time": "2021-06-17T12:39:32.846486",
     "exception": false,
     "start_time": "2021-06-17T12:39:32.827245",
     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "**Learner**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "0ec12c94",
   "metadata": {
    "papermill": {
     "duration": 0.027901,
     "end_time": "2021-06-17T12:39:32.893799",
     "exception": false,
     "start_time": "2021-06-17T12:39:32.865898",
     "status": "completed"
    },
    "tags": []
   },
   "outputs": [],
   "source": [
    "import torch.nn as nn\n",
    "import pytorch_lightning as pl\n",
    "\n",
    "class Learner(pl.LightningModule):\n",
    "    def __init__(self, t_span:torch.Tensor, model:nn.Module):\n",
    "        super().__init__()\n",
    "        self.model, self.t_span = model, t_span\n",
    "    \n",
    "    def forward(self, x):\n",
    "        return self.model(x)\n",
    "    \n",
    "    def training_step(self, batch, batch_idx):\n",
    "        x, y = batch      \n",
    "        t_eval, y_hat = self.model(x, self.t_span)\n",
    "        y_hat = y_hat[-1] # select last point of solution trajectory\n",
    "        loss = nn.CrossEntropyLoss()(y_hat, y)\n",
    "        return {'loss': loss}   \n",
    "    \n",
    "    def configure_optimizers(self):\n",
    "        return torch.optim.Adam(self.model.parameters(), lr=0.01)\n",
    "\n",
    "    def train_dataloader(self):\n",
    "        return trainloader"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c83672c4",
   "metadata": {
    "papermill": {
     "duration": 0.019388,
     "end_time": "2021-06-17T12:39:32.936640",
     "exception": false,
     "start_time": "2021-06-17T12:39:32.917252",
     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "**Note:** In this notebook we will consider the depth domain $[0,1]$, i.e. $t\\in[0,1]$. Note that, for most architectures in *static* settings (aka we do not deal with dynamic data) any other depth domain does not actually affect the expressiveness of Neural ODEs, since it can be seen as a rescaled/shifted version of $[0,1]$. Please note that, however, other choices of the depth domain can indeed affect the training phase\n",
    "\n",
    "The depth domain can be accessed and modified through the `t_span` setting of `NeuralODE` instances."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7397e706",
   "metadata": {
    "papermill": {
     "duration": 0.019488,
     "end_time": "2021-06-17T12:39:32.975753",
     "exception": false,
     "start_time": "2021-06-17T12:39:32.956265",
     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "## Vanilla Neural ODE (Depth-Invariant)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6d3ec4d3",
   "metadata": {
    "papermill": {
     "duration": 0.019643,
     "end_time": "2021-06-17T12:39:33.014980",
     "exception": false,
     "start_time": "2021-06-17T12:39:32.995337",
     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "$$ \\left\\{\n",
    "    \\begin{aligned}\n",
    "        \\dot{z}(t) &= f(z(t), \\theta)\\\\\n",
    "        z(0) &= x\\\\\n",
    "        \\hat y & = z(1)\n",
    "    \\end{aligned}\n",
    "    \\right. \\quad t\\in[0,1]\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6923c9a3",
   "metadata": {
    "papermill": {
     "duration": 0.019468,
     "end_time": "2021-06-17T12:39:33.054014",
     "exception": false,
     "start_time": "2021-06-17T12:39:33.034546",
     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "This model is the same used in [torchdyn quickstart](./00_quickstart.html) tutorial. The vector field is parametrized by a neural network $f$ with *static* parameters $\\theta$ and taking as input only the state $h(s)$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "60b4c046",
   "metadata": {
    "papermill": {
     "duration": 0.03442,
     "end_time": "2021-06-17T12:39:33.108134",
     "exception": false,
     "start_time": "2021-06-17T12:39:33.073714",
     "status": "completed"
    },
    "tags": []
   },
   "outputs": [],
   "source": [
    "# vector field parametrized by a NN\n",
    "f = nn.Sequential(\n",
    "        nn.Linear(2, 64),\n",
    "        nn.Tanh(), \n",
    "        nn.Linear(64, 2))\n",
    "\n",
    "t_span = torch.linspace(0, 1, 2)\n",
    "\n",
    "# Neural ODE\n",
    "# `interpolator` here refers to the scheme used together with `solver` to ensure estimates of the solution at all points in `t_span` are returned. \n",
    "# During solution of the adjoint, cubic interpolation is used regardless of `interpolator`.\n",
    "model = NeuralODE(f, sensitivity='adjoint', solver='tsit5', interpolator=None, atol=1e-3, rtol=1e-3).to(device)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "10f31709",
   "metadata": {
    "papermill": {
     "duration": 16.239834,
     "end_time": "2021-06-17T12:39:49.372314",
     "exception": false,
     "start_time": "2021-06-17T12:39:33.132480",
     "status": "completed"
    },
    "tags": []
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "GPU available: True, used: False\n",
      "TPU available: False, using: 0 TPU cores\n",
      "\n",
      "  | Name  | Type      | Params\n",
      "------------------------------------\n",
      "0 | model | NeuralODE | 322   \n",
      "------------------------------------\n",
      "322       Trainable params\n",
      "0         Non-trainable params\n",
      "322       Total params\n",
      "0.001     Total estimated model params size (MB)\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "c9dc8516c38a441da216c574faa87055",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Training: 0it [00:00, ?it/s]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# train the Neural ODE\n",
    "learn = Learner(t_span, model)\n",
    "if dry_run: trainer = pl.Trainer(min_epochs=1, max_epochs=1)\n",
    "else: trainer = pl.Trainer(min_epochs=200, max_epochs=250, progress_bar_refresh_rate=1)\n",
    "trainer.fit(learn)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e83d9623",
   "metadata": {
    "papermill": {
     "duration": 0.020305,
     "end_time": "2021-06-17T12:39:49.413997",
     "exception": false,
     "start_time": "2021-06-17T12:39:49.393692",
     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "**Plots**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "id": "d18a1e08",
   "metadata": {
    "papermill": {
     "duration": 0.18947,
     "end_time": "2021-06-17T12:39:49.623851",
     "exception": true,
     "start_time": "2021-06-17T12:39:49.434381",
     "status": "failed"
    },
    "tags": []
   },
   "outputs": [],
   "source": [
    "t_span = torch.linspace(0,1,100)\n",
    "t_eval, trajectory = model(X_train.cpu(), t_span)\n",
    "trajectory = trajectory.detach()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "id": "82c5f886",
   "metadata": {
    "papermill": {
     "duration": null,
     "end_time": null,
     "exception": null,
     "start_time": null,
     "status": "pending"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x144 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Trajectories in the depth domain\n",
    "plot_2D_depth_trajectory(t_span, trajectory, yn, len(X))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "id": "a3a8bbcf",
   "metadata": {
    "papermill": {
     "duration": null,
     "end_time": null,
     "exception": null,
     "start_time": null,
     "status": "pending"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 216x216 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Trajectories in the state-space\n",
    "plot_2D_state_space(trajectory, yn, len(X))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "id": "433164d6",
   "metadata": {
    "papermill": {
     "duration": null,
     "end_time": null,
     "exception": null,
     "start_time": null,
     "status": "pending"
    },
    "tags": []
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/michael/libraries/torchdyn/torchdyn/utils.py:181: MatplotlibDeprecationWarning: Axes3D(fig) adding itself to the figure is deprecated since 3.4. Pass the keyword argument auto_add_to_figure=False and use fig.add_axes(ax) to suppress this warning. The default value of auto_add_to_figure will change to False in mpl3.5 and True values will no longer work in 3.6.  This is consistent with other Axes classes.\n",
      "  ax = Axes3D(fig)\n",
      "/home/michael/.cache/pypoetry/virtualenvs/torchdyn-voYSR01p-py3.8/lib/python3.8/site-packages/mpl_toolkits/mplot3d/proj3d.py:136: VisibleDeprecationWarning: Creating an ndarray from ragged nested sequences (which is a list-or-tuple of lists-or-tuples-or ndarrays with different lengths or shapes) is deprecated. If you meant to do this, you must specify 'dtype=object' when creating the ndarray\n",
      "  return np.array([xs, ys, zs, np.ones_like(xs)])\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x216 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Trajectories in space-depth\n",
    "plot_2D_space_depth(t_span, trajectory, yn, len(X));"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4e1e0ff4",
   "metadata": {
    "papermill": {
     "duration": null,
     "end_time": null,
     "exception": null,
     "start_time": null,
     "status": "pending"
    },
    "tags": []
   },
   "source": [
    "## Vanilla Neural ODE (Depth-Variant)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "85712e55",
   "metadata": {
    "papermill": {
     "duration": null,
     "end_time": null,
     "exception": null,
     "start_time": null,
     "status": "pending"
    },
    "tags": []
   },
   "source": [
    "$$ \\left\\{\n",
    "    \\begin{aligned}\n",
    "        \\dot{z}(s) &= f(t, z(t), \\theta)\\\\\n",
    "        z(0) &= x\\\\\n",
    "        \\hat y & = z(1)\n",
    "    \\end{aligned}\n",
    "    \\right. \\quad t\\in[0,1]\n",
    "$$\n",
    "\n",
    "This model, contemplated by the seminal paper from [[Chen T. Q. et al, 2018]](https://arxiv.org/abs/1806.07366), is usually obtained by concatenating $t$ to the state $h$ as input of $f$, i.e. $f([h(t),t])$. For a simple and flexible implementation we developed a dedicated layer, `DepthCat`, which takes care of automatically concatenating $t$ to the state at each call of the `DEFunc`. The final user only needs to specify concatenation dimension to which $t$ should be appended. Specifically, for an MLP, $h\\in\\mathbb{R}^{batch\\times dims}$ and, thus we should use `DepthCat(1)`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "id": "f8d2530b",
   "metadata": {
    "papermill": {
     "duration": null,
     "end_time": null,
     "exception": null,
     "start_time": null,
     "status": "pending"
    },
    "tags": []
   },
   "outputs": [],
   "source": [
    "# vector field parametrized by a NN\n",
    "f = nn.Sequential(\n",
    "        DepthCat(1),\n",
    "        nn.Linear(2+1, 64),\n",
    "        nn.Tanh(),\n",
    "        DepthCat(1),\n",
    "        nn.Linear(64+1, 2))\n",
    "\n",
    "t_span = torch.linspace(0, 1, 2)\n",
    "\n",
    "# Neural ODE\n",
    "model = NeuralODE(f, sensitivity='adjoint', solver='tsit5', interpolator=None, atol=1e-3, rtol=1e-3).to(device)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "id": "563c5655",
   "metadata": {
    "papermill": {
     "duration": null,
     "end_time": null,
     "exception": null,
     "start_time": null,
     "status": "pending"
    },
    "tags": []
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "GPU available: True, used: False\n",
      "TPU available: False, using: 0 TPU cores\n",
      "\n",
      "  | Name  | Type      | Params\n",
      "------------------------------------\n",
      "0 | model | NeuralODE | 388   \n",
      "------------------------------------\n",
      "388       Trainable params\n",
      "0         Non-trainable params\n",
      "388       Total params\n",
      "0.002     Total estimated model params size (MB)\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "a901f10846354e8ea380f3db19a72cd6",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Training: 0it [00:00, ?it/s]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# train the Neural ODE\n",
    "learn = Learner(t_span, model)\n",
    "if dry_run: trainer = pl.Trainer(min_epochs=1, max_epochs=1)\n",
    "else: trainer = pl.Trainer(min_epochs=150, max_epochs=150, progress_bar_refresh_rate=1)\n",
    "trainer.fit(learn)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0570f62a",
   "metadata": {
    "papermill": {
     "duration": null,
     "end_time": null,
     "exception": null,
     "start_time": null,
     "status": "pending"
    },
    "tags": []
   },
   "source": [
    "**Plot**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "id": "c83451f8",
   "metadata": {
    "papermill": {
     "duration": null,
     "end_time": null,
     "exception": null,
     "start_time": null,
     "status": "pending"
    },
    "tags": []
   },
   "outputs": [],
   "source": [
    "t_span = torch.linspace(0,1,100)\n",
    "t_eval, trajectory = model(X_train.cpu(), t_span)\n",
    "trajectory = trajectory.detach()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "id": "39a829ff",
   "metadata": {
    "papermill": {
     "duration": null,
     "end_time": null,
     "exception": null,
     "start_time": null,
     "status": "pending"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x144 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Trajectories in the depth domain\n",
    "plot_2D_depth_trajectory(t_span, trajectory, yn, len(X))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "id": "19490a35",
   "metadata": {
    "papermill": {
     "duration": null,
     "end_time": null,
     "exception": null,
     "start_time": null,
     "status": "pending"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 216x216 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Trajectories in the state-space\n",
    "plot_2D_state_space(trajectory, yn, len(X))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "id": "73e5c0e0",
   "metadata": {
    "papermill": {
     "duration": null,
     "end_time": null,
     "exception": null,
     "start_time": null,
     "status": "pending"
    },
    "tags": []
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/michael/libraries/torchdyn/torchdyn/utils.py:181: MatplotlibDeprecationWarning: Axes3D(fig) adding itself to the figure is deprecated since 3.4. Pass the keyword argument auto_add_to_figure=False and use fig.add_axes(ax) to suppress this warning. The default value of auto_add_to_figure will change to False in mpl3.5 and True values will no longer work in 3.6.  This is consistent with other Axes classes.\n",
      "  ax = Axes3D(fig)\n",
      "/home/michael/.cache/pypoetry/virtualenvs/torchdyn-voYSR01p-py3.8/lib/python3.8/site-packages/mpl_toolkits/mplot3d/proj3d.py:136: VisibleDeprecationWarning: Creating an ndarray from ragged nested sequences (which is a list-or-tuple of lists-or-tuples-or ndarrays with different lengths or shapes) is deprecated. If you meant to do this, you must specify 'dtype=object' when creating the ndarray\n",
      "  return np.array([xs, ys, zs, np.ones_like(xs)])\n"
     ]
    },
    {
     "data": {
      "image/png": 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274e//13n4Ydhxw5IpxW5KypgyhSYNEmRPJFQpDYMRdZQKK+6p9Mq281x8q8JoQgvhHqtoUFJ9mhUjX8kDLWNFQeU5FW5eERlZSUXXHABL774YgeSV1VVsXv37vbne/bsaX/PuyHwro8upFKwZg3ccYfB2rUGbW2KxGPGwLRpMHVq3pGm6+qYpql4eDqt7n172ye3lOp111XHNC0vyf0FYtq07s9xKGXFDWgVWnNzM4lEgmQyyerVq7n22ms7nHPeeedx880387GPfYw1a9ZQXFx8WFW9EIF3fXRAShUKu+MOndWrBfv3q9fLymD6dHUbN04R0jAUaR1HedIzGbU4+K/5kto01UJgGOpxLKYkvf+av0hEo1BXpz4vGu3efIdKVtxASvKx73nPewAVU7zkkks4++yzO5SbnnPOOaxcuZIZM2YQjUa57bbbujVw4F0f+Whqgvvu07jrLo0tW5REjsWgutpj7lyDysq8B9x1lW1dSGrfDg+H83HyUEg9tyx1bxgd89b9x0KoMXbuVI97QnI1n8HNihswkkspt3X1+he+8IX2x0IIfv7zn/d47CB3feTC81RCyx//qPPCC4LGRkXGceOU+jx+vCSRUJK6pYV26R4KKVIXFeXj3/F4PgnGD6n59rem5VX0zk7xQrW9p0ltQyErbkiF0HqLwCYfmdixA37/e41VqzT27FESurhYecsnTYJIxCOZVI4zP8ZdXKwkfDyuJLRtq1ttrUpp7dzYxSe1n/DiP/fDZb7K7t+nUur+MKkeXWKws+JGDMkDm3zkoLUV7r9fcOedOm+8oSS0aapY9aRJKqSl0lEFhiHRdSWhLUtJ59ZWdfMlr29v++EzXVc3X3pDRwnu59f4DjnPU/fZLGzfrs5973uPXJJaiMHMihsRJLcsi2x3q/4DDFnYNmzYAL/5jcELL6iYNygCV1VBaanEMATptFLHo1HRbmOHw/kUVctS0tz3qut6XjXvbBL7r/kk9+8Lye8T3TDU88rK/ELQEwzWVskjguR+AkKA4QkpVQrq73+v8fe/a+zenVeLi4pUrDseB9NUpK6ogGhUEotJLMvDsjqSOZvNJ7P42Wt+Zpsvxf3HvqQvPN55IfAluk92357vDQZjq+QRQfIAwxeNjfDooxq//a3WrpqDIlxpqZKaRUUqTFZSAqYp28nc3CyQUiMS6WhT+9LYl96FMe/CW2GIzCe6/zwU6qgZKM0hnya7f38+XNdTdCZ6f3vcBzJOPvG0007jwIEDCCH43Oc+xxVXXNHhnCeeeILzzz+fqVOnAnDhhRe+I5YeYGQgk4G1a+G22zSeflqjvj7fZy0SUYktlZWK6NGoIpvjgOMITNPfe16JUz+hpVAd7yyRfaJDXgX3pXFnld1/r6blCR6J5CW979ibNw9mzuzd9Q9kVtxRkVzkZia7pys7N954I4sXL6alpYUlS5ZwxhlnMG/evA4n9WbTw9xcevyeAAMPKVX7pXvu0bjvPo2aGqWa+ygpUfZ3ZaVPLImmCWxbqrJPTeC6YBiCUEhgGF6H0JhPxkLpLERH0vtZbYX3jpP3xNu2WoSEUAtPOq00Dv/9hqEWnzFjVPpsb6NiA5UV12OSCyGqgRRQ301yAyCl3Oc/TiQSzJ07l5qamneQvDeQUuJ5Hv/4xz8444wzCB2pQVeAQcGuXfDAAxoPPKDx6qsdmzIYhrK9J09WcW9dF7lkFUEkopxrRfFWSq06isZXEY0JLMvLkdxod4r5UrpQavvwveT+OT6kVEQvfC6lWnz8m19/7qfFCqFeSybVwtRbDIRE740k/zegCTgkhHCAJNAC1AE7pZT7jzTAjh07eOmllzjhhBPecczf9HDChAn85Cc/Yf78+e861sc//nHefPNN9uzZwzPPPMN73/vegORDDA0N8OCDgvvv11m/HurrO5KsqEipvRMmgGUJioslFRUepaWSoiJBNCrRZBZv75O4mTbs7AdplbGcTS6IxfKS2pfghSq4T2z/HN8WlzIv6Quz3fyU13BYEbhw0fBz3P1imKPdUKVwq2THcfolK67HmysIIU4AFgAzganAdGArsA0oAq6WUrYe5u2ytbWVU089le985ztceOGFHQ72ZtNDPy/4vPPO40c/+lG3CloCDAySSXj6acEdd+isWaNCYoUSU9dhxgyYPRuKiyVFRTIX9tLai0VA4roSI/k2RssahBCICeegaVmE04wWrcaKxTrY0b7jrDA2bln5ZhD+a4XwpbyfCOM77nzC+4uFb7P7HWMmTsw3nTga+BsrGoZxNETv8k09npqUcg3Q3q5FCDEFuBJ4FEXyw65ttm3zL//yL1x66aXvIDioTQ99nHPOOXzpS1+itrb2sJ1kIJ8mGOSvDx3YtnKq3Xqrztq1gr17lY1biJISpZpXVSlp1tIiaG0VBR5u2U5WI3sQ0fIq0m7BwMU78AxG1FSSNxxF02IdElN8O7qwXFTKjp5zw8iXjsZi+Ti736HVd+b5ZPfn5Xn5Y34lWzZ79CTvz6y43tjkC4E40Ay0SSm3CSFOA26WUm5+l/eJyy67jLlz53LllVd2ec7+/fsZO3YsQogeb3oYpLYOPjwPXn0VfvMbjRde0DhwQBWWFMJ3Wo0fT3vOuaYpovk3w4BQSHnRI3ojodrHMPVNmLSga2k0sQFNSER0IW5lOcaYKjy0Dplq0DF8BuqzPC9fP15fn3e8+eQPh5XnPJFQc4lG1THfCVco7YXIN6LoC/RXVly3RxFCaFJKDyW1xwKbgTqh4hhvA07uPHEYh9zJf/zjHznmmGNYtGgRAD/4wQ/YtWsXcPSbHgYkH1y89RbceqvgiSd09u9X8e5cTUY7/IaJEycqz3RRkUpuCYUk4bDskCOuaSCkQ+bABrzmGmxPQxMWumaiaw6a5mI4LRjxGkLZcYQqJhON5u1u33Puq/2uqwjr29Cdk1oyGSX902mVEltTk1f9i4qU5lFSosbw02cdR/VynzevZymu74b+yIrr1YaHQogIyi6fAVQCj0gpX+/GW/stLe1b3/oWxx9/PKeffnp/fUSALrBnD9x+u+CRR3R271bk7qyaC6Gk4rhxKuRUXCzbJbVP6sIEFU0DQ/fQWt5ENL6AyDYhtSx44EkN6Wl4GAitHIomohfPgugEDEO0l40WSuSiIqWK++R3XUX+bLbjguBLfr87TDqd96in0+paTFMVwZSXKyleVKR8Cn2duKbyANTGij3A0dvkQohJQK2Usg1YK4RoAXblng8qAkk+sGhogDvugHvuMdi5U9Vv+0QoRCikiDBpkop/x+O+A0y2J5qEQrK9iETdS8LOTsLy70Ss7eh6E2EjjaFnsEwbU3Nx5Hiy4UnYcRN33Em0ZUQ7KTMZFdc+dEjNwSdvNKoIWlysNIrKSvV6NpuPj7tuXsL77Zl9OdjWlr/V1eUdebW1MHduzyrTjoS+zG3vFskLVPXPADVCiCcBE/gO8Gfg7wXnDAqCTQ8HBq2t8Le/wYoVBlu3Kps7m31nKMnPFotGFaEA9uUyJaQUHTLUNE10yDYzZBojnUS3l2IYc7GMFJaexTRtIqEsIUMjUWyQKLWIV06kvNyjvFyR0s9V9+PcLS1qAWppUXOvrVUpqVLmO8H4iS1lZer9mUxH0udMZGIx9Rm+M8+vdtu1q2etoQYa3ZXkvhpgApcA0wAdFTrbDDCYBIdAkvc3kkl45BH4/e8NNm1SkryzWl4I3x7OZJREravLF4oUZqF1rvwSgG43oTkGhlaGqccxhI2uuRiGg65LQiELo8HErAHdKiK8RSMczVefVVQodXrsWPXYj6r6xG9tVYtTQ4Mi/549sHt33uPuv6+kJO9w80nvd3L1Jb1vp/ux875ywvUluktyn8APAb+VUr7dT/PpNeLxOPX19YM9jRGH1lbV6tjvzOKXfx4J/qYG/pZDfvtjP+W0sCLMMNSioAsPUvtwW7fhZLM4jsBDx3FNsl6IVFagixA4FkZWENLThKIhUlqaUMzEslQOfE1Nvobc39SwslJ59CdMULfq6jwxk0lF9tpadb1vv616yYVCiuzjxilJX1yszlc59PlU2OZmtRiMHdu3331fJcV0i+S+t1xK+VTuw3VyTrTBluA+Aknet2hqgnXr4A9/MHjiCSX1ugtNyyec+Oquf1/YacWy8vnmYQssvYFw9nXCif2EQ02Yuo2h2XhC4HkGWaecFGNIOSWk0gapbIRUJkyq0YUkaLnuMH7FmO9kS6XUJgmvvKKOlZUpwldXq1txsZr3pEl5R1tDg9I+6uvVe0OhfF69igzku71ms+pzh2r5RK8CcVJK98hnDSwCkvcNGhuVWv6LXxisX9+7MQprun2vc2EmmV/nXdglVeASslsxGYNpxAlpGUJGipiVIhrOEDYhXqJTGc0Qs3ZjWh4ZL0HWayGtT6QxXUJbLvxVuIGhYeQbN1qW0hjq6lT23auvKnKOG6fCetOnK4kPSoJPnKgI39yspHxjI7z0Ul47qK5W5/vqel2dkuZDbCu0ga8nX7VqFVdccQWu6/KZz3yGq6++usPxTCbDJz7xCdavX095eTl/+ctfmDJlyhHHDVpA9R6uq5olXnedYMOGo/fo+uTtTGyf9H4PdMdR0lDXQfeaSdsCMxRFYGIZWSwjSnPaxWiRmJZJqNUgEraJhG2ssEk8ConSCBXjS5lcolYT39nW0JDfiri5WWkmvoc9Gs076UDZ47t2qV7uFRVKos+erSS2lMqbPnZsXrU/dEiR/sABtUiMHat6vRcX9y3BB1Rd7yu4rsuXv/xlHnnkEaqrq1m2bBnnnXdeh0q03/3ud5SWlrJ161ZWrFjBVVddxV/+8pcjju2ntXqeN2T2oBpqkFJ5lt98Ex58EO66y89I0zlMiLVX8O1V6Nhjzfd8Fy4AAF6qBY0kUkgyjokmdWw7REqTaHiYYbA8A9PzyGZtGltNTMvAsCThZBGxllg7cf3wWHV13tFWX6+krO8N95/7sfSiIkV8TVPkPXhQSeyKCiXdZ81SRPa3USorU/H+1lb1fe7bp5x3DQ2wdGk+mjBUMKAkf/HFF5kxYwbTcvGGj33sY9x///0dSH7//fdz3XXXAXDRRRfxla98pT0xoCvs27ePW265hRdeeIEXX3yRRCLBDTfc0O/XMtQhpXJAPfecUr+fe06we7dGX5K5O/C90ul0vnuLXyxiWWAaWQy3EUNrIRTOoGkumnBxCeM6GlkvStYxyHgWesbG1KMYFlieICQtMloRqaxHyLRpiISIRER7HnppqSL+5MkqxOWr3gcO5MNqjY3qZpqK8CUl+TBZXZ06d9065aybOVMV1JSX5zWGkhJ1fX6KbEPDKCd5Vxsadt6auPAcwzAoLi6mrq7usEUqoVCIxYsXc9ZZZ/Ff//Vfo5bgnqekyVNPwQMPwPPP6zQ19R2hC21rPw5dWPThO9T8udh2viyzMKvMl66mCY4twU1jiBAhrYiQ6aDrGUKGg2XahEMZEiGJ0E1c18b2dGw3TCqjY7sWMh3CbEsTs2xCkSiOZ5JKifb2zI2N+ey30lJFyMpK5TzzG0H4+fWtrfmYup/A48feXVd9t3v2wAsvKNV87lylLQih3u/b5ZFIx9LUoYAh5iLoOcrLyzn//PNpamoadRsstLXB5s3wt78JHnhAY/du8Y588Z7AD3n5pDUM9WcPh/NFHIaRl4K+je17zv09xnzPeaFK7nu5fY+354GbsRGuIEsIz9CwXRMwMAwP05CEQhphR2IaHpZlEw17GGYaoUfJaCbpVhs3a9OcFegZDTOtteeWe54ism8mtLYqNTwSUWQvLVUOt+pqZWfX16vjzc3qVlenbtGoOn/MGDVOW5vqbPPmm2rBmDtXqfPl5eozoO9IPixt8u5saOifU11djeM4NDU1dasSbbQ43traVBz3r39V7ZN27+5Yo90b+BsSqIaIEssShMOS4mJBUZEiSlmZpLISbFuQTKo/9aJFHlOnejQ0CDZvhs2bBdu3C/bsEdTX077xgZR5L7dlgSYk2dZG2pIpMlkdTxq4joHteWhS4EmJJzUcT2A7El1zMbMRDFN1iQmFw5hhKC1qRndacEWENi9O2pE0NopcFVveo+66ecKHw2qBOnQon+1WXq5U+upqdezAAUVwf6ul/fvVIhCL5XvP+V76xx9X6vyMGXDMMeq7HGouoQEl+bJly9iyZQvbt2+nqqqKFStWcMcdd3Q457zzzuP3v/89J554InfffTfvf//7u7WiGYaBe7T/9iEKx1Gx2sceE/zhDzqbNnWdJ34k+BlmvqodieSLN8JhX/KKXI53vuNKWZlyPEkpyGZhzBjJ4sWSpUs9wmFVF37sseA4EttW5N63T/Dqq/Daa4ItWwR794r21FJcF0smKQ3XYyWSOK5JKhMhbcfIuBFsJ4QrBY6j4TguhmmQ9QSWC2nXwrJ1zLYMYd3F0gXh4iglUQ8hPBxPb9/g0C9z9RtBRqNq0QmF8m2dmpoUqYuKOqa3ZjKK2Pv2KTu7rU2d29KixiktVY45XVevbdigJPyMGXD++fnY+1DAgJLcMAxuvvlmzjrrLFzX5dOf/jTz58/n2muvZenSpZx33nn867/+K5dddhkzZsygrKyMFStWDOQUhxRaW5U6vmKFzgMPqF08e9NuyCew/15fDU8k8p5v37b2O5H6/TtKSmDCBIltC1paJImE5JhjlBQvTOEs3CssGlULwYIFkMlIUilF+pdegg1rUmx7dQf79pskM8W0pEvQjQzRUDPliUM4REjZJaTsYlLZMFlHx3ENwMWRJiYGWdvG0rKkMTGtOGE3RCTlYCXCmLmkFd/+b21VxE6l1OITj+fNhUxGzdd3DDY2KpW9rEwRuLpaqfT+QnDoUH68PXvU87IytTBUVORV/aNtCZX/TvtGXe9VqelRoF8/bPHixTz55JP9+REDgtpaeOUVwe236zz5ZPezzfyCD79/marwyncxgTyJ/ZRPy5KAKtH0k0YSCXVuPC6pqpI4jkZLiyQSkcyfD8cf71Fa2vPrctJt2Jt+RdObD7JlRzHPbV7EqzsWs7N+Is2txTheCNPwiMVtiiJpPClozhSRbIuTyoZxZDi3Q2gGkwyGJjAtC11PYhghjGgJVlhrNz00TV2/n5XmS3g/I6/dfNDy30dh19eSEkViv71Tc7NaBHxnne9j8BdNfxPGRYuURD9atb2HZabQV+2fhjKGe1vmQ4dg7VqNP/1J4+mn39lVpRB+KyK/FrtwKyC/BNLvReZnmMXjSo30M8HUOXmCa5qktFTkGixIxo+XeJ5GMikJh9Ufd9Gi3hEcz8E8uIpw419JFO2h6phGls95hua2ONv3T+a5t05h7Y7T2Fk7nZZ0Mc3JYizTpag4w5iKJrJS0NQiaGl2yKZcso6JK0zsNhvT0DBCBqYBjqsI3dyc3z7JD49FInkHYDKppLdlKYL6RSeplFoIbVstCr5099X4mTOVhK+vV9LcJ3tjo1Lb9+1Tv8u0aUdH8r78L48okgPvGlMfqqitVeS+4w6NJ59Uf5jOKKzegny4qtCD7ZdqFkpvfzMAv+xTiPyGAZDvdBIKqc6oUipCVFVJQEnwUEjZ3YsWeb0rwpAS0fgS+q5bIV0DtCAEREJpIqE0lcW1HDs9yaXGLt7cN5dnX5nGS5tns/PQeGqbSjnUFCKR0CiNNzIuUUsyqdGYHUdbiyCb8XDcKI5j4LR5hCzVBNI08/uS+/a43znG38q4rU0R3c9cSyTUOX6TCP87amvLF7D46rnf3aauThG7vj5f4VZbm5fwQwFDZBp9g0gkQiqVItrdXeIHGU1N8NJLgr/8RWf1avXn6Gw9+V1FCzcHKJTehSWbflWXL9H9P7jfLcV/zW9f5Kvt4bAkFlMEV7ncHkIImptlrh+65NhjJQUpDj1D2170bb+ClrfAawM6OkiFqCRSVkY4pjOm8k2Wzt3DodROXt05jSc2LmLT29UcOOCyZ69FWJRSVOoxeVwrblE9TakS6lrHkLY1XAcy0kNoWnvDRT+819aWb9oYjSoC+rujZrNKstfVKTL7deN+P7hwOG/D+xlz/hZOfv76oUN5L7zjqN9yqDQOHlEk94tUhjrJ02l44w247z6De+5RnnO/MQF03HzvcMknnXcF8dVzyEtrn+T+OL69KUThTiOSRELgeeo948Z5mKb60xuGCi8dc4xk2jTZu9ivk0Tb+UeoWwNOC9C5CD0BofFIazxCgtA8oqVRJo9xmDAjw0lnu+za9jprnm7i2TUJ3j5QTV1TGXUNLRSF41SMFVRWZ2lOCmobIrS1aWQySqoaRr51sr9YZjLq2nxV3q8h93ust7bmc959B6Tf/TUaVb+B3weusTFfxjpxoro/eFAtCEdL8kBdPwz87jDv1sJ5MOF5sHMnPPKIzp13Cl5/veMWQYW2dGEfcd9TXFiDXUjyQpXdf7/fdth/j+9h9x/7fcljMdFuo5eXe7mED/UHKy6GBQskc+bI9gWkZxdsI3bfj7b3XsjWA52rBC0wqiAxEYwQeElkaAxCK0ZGKtGL51AiWimd8gqzrdc4Z3kFG/edweP/3MZrmys52FpOc02EWJFGRbnG7FmCZFu+Ysxvl+wvkr76DmpR9VV3//vwF8HiYkXyxkZ176v32awa0zd7fA2huTkv2SdPVouAb+MPBctxUEn+jW98g7///e+EQiGmT5/ObbfdRkkXe85MmTKFRCKBrusYhsG6deu6HC8Wiw3ZrLf6enjhBY0VK5RTraEh7/EurL+Gjs39fXL7GWiFpPYle2GNtn9fuGNnKASmoeqt85sMyBzBlQ+jrEwSi0Emo6R6JAJz50rmzPHabdMeQXqIurXoO2+D9H7URjuFECDGQ9FkPCOG5rWBUQJWGdIsRsZmI40oeuMryOY3iEZdJlTNZuz4Jzmpag/b6o9l1UsnsW5TFfv2h9m1WxKulZSXC6ZMUYQ8eFARNZXqSHY/e88087HvoiL1exQ2tCguVsfr6xWRS0rydeRtbUrS+2W1vgbgd6XxF4KhgEEl+RlnnMEPf/hDDMPgqquu4oc//CH/9//+3y7Pffzxx48ooYdi1pvjqHbF996rc999gp07822T/I4phcT17WY/lltIWF8y+1LCMPIqp65JhHDRhYcpbEzhomsOBi6W56B5krApEa7AlJJY1MN0QjiYlJQKisKCTCqE7ZqYps7s2TBvnkcs1ssLb92Jtu0WaNsGspV37rkxDuKTkWYxmrBBiyHDZWDEkLHpeOFx6K1vIZteQ3NacUuPR7NrMbKbCY0dS/HsMUxe0sYFTUmefV7jqSdSbNsdZ2+NRV0dlJdr7Vlse/cqsre1KUL6kQl/o0PDUGROJvMVaX7FnN+RtbExb7OXlSmC+x56n+y+KeB79pNJev39jRh1/cwzz2x/vHz5cu6+++5ejfPyyy/z5JNP8txzz/HUU0/x05/+lOXLl/fVNHuN2lp46imNv/xFsGaNoLExLy18tblwX2y/cb/fHtjfd7uQ6H5SXyTsEQln0EQW08sgpY3uZVUvNOFhSonhuhi6RwiPkOaiuQIdSTRkY2bAdTVKyrKUkyHbEMHJWJiWxcxqwYLJGiXhGDgJ0MMgeqCvZ+rR3v4VouFFcJOA3emEcohXIyNjENIDNKRVAlocYtPwimagt+5ANr6Glj2IF5+L0EJojS8ijQQUz0eLjaUoEaW8ymDa2Lc4feEBnnu5mkfWzGL7LqvdCVZRoVToqirlRa+t7djCKRRS37fnqccNDXmb3e8sa5pqnNJSNeaBA4rs5eXqWEtLPkznx+I9T4Xber1I9iGGjE1+66238tGPfrTLY0IIzjzzTIQQfP7zn+dzn/tch+O7d+8mHo9z/PHH8773vW/QCe5L77//XefeewU7duSbI/jS25cUkE/a8J1vhef5trdhgJ22kXaWRChJ1GxFc7JoeKgcI4nQIWR4hEwBAgwTzJBL2ACEhmkKwpaLoRs46MSLXUqLdWw7RiqrYYgMkysOsqj6AOO1JPJAFMwSpFUBVgXSLAazCLR30d+dFNrOO9AOrga7mXfa4REwxyFD4xFCILHBqgS9GKIT8eKz0VIHoeUNtLYdyGgVMjIFve5JJBoyMRcZmwqhUpAR9OxeEvp2YtM0xk/L8J5zXJ5bI3jkEZXjv3evIvb48aoZxPjx6rW6OkV2v4ONv3j6BTeep9T8RCKfGej3cctk1Pv37FFSvqxM/Ub19UoLiMfzu7QMBfQ7yYUQjwLjgA47lH7/+9/n/PPPb39sGAaXXnppl2M888wzVFVVcfDgQc444wzmzJnDKaec0n783HPPBeDgwYODnr/e3AzPP69x550azz2nJINt573dvmPM95D7N/+P5aeWahpoAgzDRrNbybZk8ZwMJdFmwqEUuAaG6eG5OkLXQAqssCRkeuBpGKZH2FIVXLoQqv9ZyMXQQEqNongbpUUZpGOQSYfQdMHYsYJ5CwTjJpcgZQLIomVqkZl9IAykUQThSmSoEmmVgVkMmpm/eM9B7P8n2p47IXMQaO307YRAmwBFU5R2IFNgVCB05WjziuaA14ZofQvRshkZKsGLH4veuEaF3hLHIBOzwSxGGnFI1iEyWwHQopUkwkXEzTbGToixfHm+ln7bNuXwPHRI1YVPnaok+549iph+C2bfx+HDL5VNpRRx/cYSkYgyA/yYeFubInppqSJ3Q0O++81QQL+TXEp5euHTzsdvv/12HnzwQR577LHD2iF+pVplZSUXXHABL774YgeS+xjsTQ937YKHHtK55x7lOW9tzVdfFTrCCjfRM4z8iu8nrWjCwxBtGF4DMtlGNivBE5QnGolGPBw3hGU52FkL3RTgSaywUs2ROqaZyRFcIhDohqeaJpqA1IhFHEoTNh5RUhkdTYeK4jaOmbGfGeOa0G0DaUaRWhTXrADpImQakW2E1q0IbRtSL4VIJdIahwyVgR5TCS87fgFte3gnwQHGQ9E0PDOG5qZBL0ZYJchwOV7RPKRmoTduhKbXwDBxS5ait74KmUPIxCxk0Vw8oxipx5HZFHryLdCyEJ0AoRLl7EtuJ1ESJzYjwrhxcMIJ8OST8Nhjqs3T9u1K+o4fr0pEW1rU79bU1DGu7levmWY+bFa4P5r/eyUS+br01lal1icSarwXXlCLQW8iEyPGJl+1ahU/+tGPePLJJw8b204mk3ieRyKRIJlMsnr1aq699touz43H4zT0pK1oH8Fx4LXX4K9/NXj4YfWnKZTefgKK33rYV88LmyrEYhAybAyvHpFtIKwlyTqQzkYQQjCurBHTcLG9MOGoS9YOgSmRSCJhSSjk4no6ITNLNCzRTIkQOqbmETIkIc3FsyEc8SiJteF5JhlbojmCkjI4Zk4zs2aAZhbjeR44GRBpdJqQuoU04rjRKQg8hNOCyNZDcwNoOxFWBdJ10HfcCs1vHMbRNgYSU5DhMjQvBXrO0RYqQcZnI0Pl6M2bkE2voEkbt+h4tORuROt23Eg1bnw2Ui9F6gmk62G0vgFeG45RgWEUoWkhaH4bnCaIVqFFqygqym/PtHw5rF6tmmrs3w9btqiMtXHjVInowYOqk05r6zv3UPNt99ZWJdX9kFoopI773WT8MYqLlVrv+2D6aCOUXmNQSf6Vr3yFTCbDGWecASjn2y233MLevXv5zGc+w8qVKzlw4AAXXHABoLZ1veSSSzj77LO7HC8Wi1FTUzNg8wclCZ57TuPOOwUvvKBUNdctkMpaPmxVaF9DvlgiarRhugfQsy3otBHSbTJ2mDa7CMNwGFvaRMhwsN0wkXCatkwMXQik8AhbYBoOrhciEspghUE3BBo64CnHmyHxNJNwWFJalEIQIpM1kAji0QwLZx5g7uRGTA+kHQY9BmYCgcCTLnhZyNaj04g0YkizGM+qRHOTkK1FNL2Jtn8lNL8KspnOGW1QCrGpyEg5QmZAC4NVClYJxGfhRCait27Ba9iAlm3CLloImVaM5CbcUAWyaAFadAIiPAaMMHrzW+A1I61SnFAJLlG0VA2kdoI1Fox8naeuKzU6Hleq+nvfqzrnrFunSNnQoAg5bpySwjU1Kk01k+lYh+6bVL5zrq0tT3Y/Hj5xonLa1dSoxWD8+Lw2MJgYVJJv3bq1y9cnTJjAypUrAZg2bRovv/xyt8Yb6LbMBw7AqlU6f/ubqp1OJtWfyt95w/egQ15FN818uqTpthIVe9CySSzdRdczCAQpJ07WjmIZNuMratE0QdaNYZlZ0nYUgY7UJJapETKzuJ5F2LKJRAAh0IWL0CSG6WCZAhdBxPQoKcoidZ2MY+AKiIY9Fs1tYN6sJKGQQEqJ5qWRMoV0TWX36nEw4gjpIZHgpNGcJGghpFWGZ1Wh7X8a0fL6YQgegfBEZKQKAUgXZLgYtCIcazJeeApa6zZk/Vr0bC1ebBaamUBvfAGMIvSKxcj4VIQ1FmkkEK1vQboGqYUhXIFuluO27sJNbUXXwurzM/shNKPDLExTJaskEsoBt369amb5+ut527yqSjVoHD9eOe18f4rfWdavbCvcMTWTyee827b6vWfOVLZ6TY1aDHqzq8qIUdf7GgNFcs9Tzpz779f5+98FW7fmK5oKmxT60rswaSWbkmTTzUTkQcJWAwY2miYJmS6eJ0hnLdJ2iLjVzLjyA0hXJ+NECOu1tGUSCJlBEymskIuhQzZrEQ23EjE9kAaGJpUnPSQxNQ1PuoQtSVFcBeedrIHnOUQswbFzGpg3J4MV0UCaaNJDagbSc0GCyDYBTUp6GyVgWAgthJQuuFlEai/6gecRdY+Al+SdBNeBCrzwWIT08BwHQhVIoxgZm4IoWkAoux/R/ArCPoSMTUGLVCEanlMe/NJjkZHJCGtMztG2DZI7kJoGkXEIqwxSBzFS2/A8gTANNCnBTYHdAmbiHb9dJKIkur8b6VNPwcMPK6Jv26Y0s/HjYeFCJdH9nVo9TxHWcfKklVIdy2bVrahI/d6Oo7SDMWOUbT7YjR1HHMn7OxlG2d+CFSt0Hn1UhWP8Vd5f6X2CF5Z5Ci9LpuEQrp0iZjYT1rMIJJohsYw00jVJZqOk7TDlsQbGlTWQtQ0cLYalZ0hmigAdobmEDAdDc3CzFpFQM1HTBjSEpyGFhmVIDGkgpYkVkiTiNgID2xF4niBiuRw75yDHTK8jZkmkNBF6CI8QyLTK1BIaSANP09HcDLh7kU4UzywGPYrQNKh9DVH3BGQP8s6cdIAE0kigeW1IMmjhcRAuh6LpyNLFYNchml5SanZkPMSmI+pfAOlB8XyIz0BEx6nQXaoG0boNCQhrAoTKkOl6ROsWQIBu4TkSisaiWWPAOHz9ghBK+k6f7ufmw0MPwfPP52vFx41Tkn/MGCXV/fi638dO1/P7nfuOuXRaqfDxuDqvqendy4UHCiOK5APhXX/2WY0//1nw/PPqh/c89YfxpbZPcCnB0BxMtxZSh0hldEAQCyWxLAehuei4mMLFdaK0phM4WIwrr6MsniLllqOZOkK6tNolaAYIPEKWjSEMHKkTjSaJhiXCC6lsN8AwsugCsLOE4xALu+iegUMI19OJhmHh3AaOnd1ALCoVaWQWHA9Igx5RUlPa4NloUiKNMFJqCLcN4exFEsZN12Hs/ztk99E1wcdAbKpSO2UzwisGT0IoikzMAacJUbcBWrdBuAIZm4NoXAteCoqOgfgcCI9XBE8fQLS8hZQOIlqNtMaA3Yho2QoyhdSL0AU45hg8axKGFkXrRvKOYSg7PBZTqvqxxyoV/q23VMitqUl5x+fNU+r8tm0qROqr634rKJ/0ra15Fd7fIbW3fuBAXT8MBiJ3/b77JE88obVvcldamv+RrRBopJHpJrRsPYaWwvU02rIRdE0SCyUxLQcND+EJwpZG0onR2pZA06G68gARI00yHcc0bBxPksmGQcuqLDbTxRACV1pEYw7RsInrRdB1G01kMXQXU9fQBIQjNmHTRgcyWQkCojGXJXMbmD+jnlhEA6Eh0EAY4OWqzNwUeGk8LYzUokjpId0UwssCFpIoWmon5r77IL0N6Or7jikHWCgOmgQ3rhLnTQv0OKJpk6orb9sF4XJkfA6icR04SUjMhaJ5EKtGhkogU6fsfSeFiFYhQ+XgtCiCe81IvRghJNKqQEvMxpE6bqYBTTfBiHTrN41EFMkTCWVPr1qlwm4HDyoVfdw4peIvWaKIvm9fviuM3146EsnHxf2NECsq6F3efx9j0PtKXnfddVRVVbFo0SIWLVrU7nDrjFWrVjF79mxmzJhx2N7qA6Gub9smaWxUpPb7hemksJyd0PoWWss2tPQBTC2N7Zqk7TiG4RGzWjFCLjoahqF6gze1JWhKFmNoDpMq9hAxsqTtEkzTIW3HabOL8YSJYZhIzcTxTFxXEDUbsWQDbiaNRgpNgGZG0KwwaBEsS2KFJJpmKCebIyiOtHDC3LdZOG0LsXAjuBlwHZAOnuvgeR4u4HgCx/Xwsq3IbD2CLJpZgh4uwwgZhLw6jEOPQno3XRM8DNZkRfBsXc6IHQOli6D0OKTbDHXPQMOLgIeMTEI0vqKy4xIzoGQuRKtU7D3biGh6FbKtEJmAtMaCm1Yqut2E1BPK52GWQGIOQg9jaBJHGriZOmWXdxOaphyms2bBJZfAl76kSK1pyi7fskVJ9unTlb3uZ7k5jlLTW1ryveL8+vT9+1WDx8HGkJDk//7v/87Xv/71wx7vzvZKMDCOtylT1A9nGiAyB7BEE5qeAakjkUgdDN2jLRPBdU0MI00snEEXGrqnYVoZXM8gmYqRtiOURJoZV7oPiUnajoBoI9kWJuPoaHqasCnwXNBN0EydaNRFEzGk4YJng5tF09IYnkR3DcJRDTMcRtN1Mo7aSHBcRSOL5+xn7uQD6IaLzEg8UqCHkVoMYZig6QhXRwgDYZgIoSOEVOEzrwmMnLfpwOPQ+gbQ3MW3Y0FomgqNySzoCTBiYJjI2BQwYoiW7ZDeC5qFJIKofR7woGiBssMjk5HhMZBpQDS9DNkmiE3KETylvOvZRqQRRwgNaapcdvQIQjqgW5hksW2JoAXNiCn/QjdhWUpqx+Pqt169Gv75T2WrJ5PKKTdunNoO6e23lQfdT41NJvPJTm1t6rW6unwRzGBhSJD8SOjO9kqQ7wzTn1i6VDlphJMlJJrQcfBkCImHabhIF5LZKJ4wCYdSKgvN0xGGRNM9ktlikqkontAYV1ZPcbSFjFOMFDquK8g4cRzHIBxKqXCNdNCkgSEcokYKaevoIQfbDhMKhcCMIDQbXW8lZKQwsRG2Qcq2MEIhplW3ctyMvUydcEiRVtNA6GiAIKPyx6WJEHGUMS9BSFQyi67S5DwHkvvh4OPQtJaus9kMoFItBm4GDEt5t6MTlZRN10DL2+A2Q3QKiCgiuQW8DMQng1mi8uPDlUpF96V7dCIyPF6p6MktkG1B6nGE0JFmDIoXKEegdJCaAdJGaDoiuQunuQ5DLEGLjuvRbyxEvs78Ix9R0v2BB1TC086dyvaeMCG/qcLmzcpW9zMXW1vzbaT27VOLQE9JPuJs8ptvvpk//OEPLF26lBtvvJHSTp0Cj7S9kuu6/OEPf+Dll19m8+bNXHTRRb2uaDsSZs/OpTo6yRwJTZAeOi62bZLORBCaJGymCGkyl5vu4WR1Wt0wGTdKxMgwtqwO0xRknZiyIx2NVMYCIYlaLlk3rLYNEjqRUBshw0Z6IHSPrG2hGxlwPCzTRdd0hB4FM0TWSyFwSISaWDClhoXzm6kYY6IbpYhctZqQAomH0FTOpvAyqgOiZ6lEGISypaVUKr3jQO0LUP8iSoJ3zmbTQKuCyBjwWgET9DKIT4PEXGSmFtGyDVL71CKgRcFtUI0ijDFgVSjd126BxlcQqb1KE4hNQkbGQ7YJ0bIF3FakHkNomnIOFi9U2oHnIIUO0gFPQHIrZsNa7NBkHBHF6OUmmJalJHcsphJdCm31ZDK/2+nxx6sdVQ4cyNvlzc2K6M3NKvOtJ82K+rpH4YCQ3C9SKSxQAVWY8sUvfpFrrrkGIQTXXHMN//Ef/8Gtt97ao/E1TaOtrY3zzz+ff/7zn/1GcIDFi6GkxKMh5WK7mgqDeYKUjOO5BprhENazOQ+7KhRvc4poS4fRNEFpvI54OIX0BMk2E9uFrGOSdaNErAzIEG3pLKGQq3LSoy5Ss3A1Q21LhI2ppRHCUwk2joahpxBOGw4GoXCY6gltLJ6xjzkTdxMxk5A1gFIw4wgZBdkGrp0zMVR4DekpCZxTeSFXIykzcOBpqH8WaOKd5QcaaJMhVKwIrkXBLAWrDIxSSO1BtL4Ndp2qHNOKIPkWSJDFC6BoLsKwkJ6NaHoNkT6gNIDiY5TzLn0I0boVpIPUIorgZnGO4BFFcARCukgpoXUzon490k2hh8HJtuEakV7vdOvb6v5+arNmwf33Kw/89u35zLYFC5RU37Ytv11SJqNCrNu3K8k/WBgQkhcUqbxr3/XPfvaz7RVlhTjS9kpCCL785S8DagOH/oRhwOTJHgdroph6lpRbRDoj0GnDEFks6ZHxdIysJEWIbKuFJwwi4RTFkRYsyyXjFtGUNnFtQcax0MmiGR6pjIapp5WHHIlpmtgOSE+iCeWcNj0dzdIRTgZPZMDwsD2LaNihvLiJOVNqOHbWfsaONdDMcpBR5bhK10G2UanFZhxhWKrii5zE9n8a6YArlb3vAQ3rof55kA10/fNNhEixCrmJkCoUSUyHyGRofVMlsAgNaY1TmkO2RlWuWeMQehQZLkPGZkH9WmjZqjSIUBE4bciW1xCZRkBD6iGE0CE0Jqeih3IElyqTznOhaRM0vozERcSngxHBqH8GOz0NreJY9KNIIg+HFZlPPlmF1f7xD3jmGUXi5mblnZ8wQTnkNm1StrifFrtnT68/tk8w6Or6vn37GD9+PAD33nsvCxYseMc53dleycdAtGM+4wx44YUoqWyUTMbv9BICJKQ9CnvcG3iYWhtInXSqDE9Y4Dkq8URIdM1DFxaG6xAOZTE0DyltUmlJJitARLDCEsuUiGwazbTJpDVcM0rcDGGYzYwv2c/06n0snF3PpHFtGHoSbAlOnZKwoTIgA3YSMvVgNyqpaobBFarkU6IS1KSSeDLbjKjfCM0voSR4ZwgwpqnQmNMIIgGJaZCYqS6/+SVIHcoldocQmSYQWdAiEJ0MiakQrlZZdc0PIt00MjEVgQleGho3qLCdVYY0xyg3QaQKWTIP0BBuVpkcwkA6bdD4CrS8qRyIkWlIPQKNG9EMC92qwM5mEZZ1VHvX67oKi/nbIk+erPwzu3YpCZ5OK7L7Trldu5Q9vmvX4PZ7G3SSf/Ob32Tjxo0IIZgyZQq/+tWvADoUqRxue6WuoGkaruse1ap9JHz0o3DddZJ0Wu0NptB1FYIDOF6EVJdOfw/wEDgIPMIhT7VvMl1MzcXUM1hWhmgmS8aCeDyCrhsURZqpKG5g0rhDzJzcxKxJdVRX1GLIZuXI0uLq5mWg7SDojUgzhtCiEDLBTUP6EHhh0IqQWigfI0cgs22Ixleh9WUO62TTq0A4gAtaMYTHQrgKaTcjMgeVBx1DNZmws+DVgR6FoinI4mMR4bGQroXWHWDvQxjFyJhqByUaN6pjwgS3DhGWUL5MqfdI8DJKNRcGMl2LaHoFkjtUllt4glqwGtchPA8Zm4RePBupadi2jWmaR0V0yNvoZ52liH7vvfDyy0pip1LKTvf3MX/jDeV8s+3ux8z7WlCNqG2SAE477TT+/Oc/U+Rv5tVP+NSn4G9/O9o10oVcZxcND8uQ6HoGy7CJRlzi4QyJeIrSeCMV8TrGVxxiYmUDUyelmTguw4SxTcSNWoRwlAosooBQHmw3DUYCRBiwlYdcN1VOuBYCKXKv24ocWhypCUSmGQ6tgcxmuo6DWyDGgK5y5LHKITIVGRqLyOyBzAFVhWKWK4lutwAOhMcrCR6uBLMU6WUQ6d3gZlVnGCMO6QOqOYRRrP4pdi0IHZmYiYhNR4YrVHWcsJDSg7ZdiObXIVsLRjHSqkDYLdC2FbCQpcepWvNwFV5kAq7rommaikr0AaRUsfOaGpX//vjjKgsyGlWLgF+FNnUqfOYz3a9G0zQNs3ela12uDoMuyfsafmprf5P817+G1atdWlo6awwOSjrbxIw00XArRdEWiiNtFBe1UhROE4+lCYcyhPQsYSNF1GwlGnMJazZmBKJhlZ1WFGmjuMSjOO4Rj7YSM5uIGnVo2KBZoCVAL1UhLyetpKXQlQdbWEAKnFZlK2sRJdndlMpwExZoniJ7thFkE0LaUP862G8D2XdcszJJ4iDSQExJzUiVCm81r8+NbSryZ2vVX84shnCu7bJVBXabUsXdJrAqkfGZKq02sw/cFqTrKG9/qBxKFqpYu5eC1C5E9hBEq5F6FFJ7Ecm31WJmliH1CKJ1GzgNYI2BkiVq8XLawKlHk2NAN3Ecp12iHy2EUE45y4KLLlLVbfffr1T1bduUB766WjnrBrPcdMSRvL8SYrxc/2TP8/A8tcPII4/At7+tU1wMUyuTVKd+xLTKN6kqO0hlcSvxmIcV8tCMXN2p1JUNKwxUS2LAc8k9UBLQdVVoSdNUmaceVX2gREi9l7HKZnVbIdOoCGqEFBn0nJc626jG1A0lEb002K3qPEwgDTINWq6LBZ5S31s3A/Xv8i1ogA2iFKwJisxtb4OdyqWvytwCoKnPDlVAbDoyMR+h6ZDcrNRwdNDKwJWI5jdzze4EeCibHA30KDJSBdYYRNsepf67aUjtQ7gp5W03YgijTFXEtb2lvsbELIgvAByEl1WJNWYxtG1Di0zBMCwcx0HX9aNW2334lW2nnKLu778f1q5VEj6ToX0P+e5akMMyhDaQ6AuSe56HlLL9VgghRPsfZP58jfvvV+oVThweeQSR2Y9ilkCRIgRejmyapuLOmqeIrumomHKuPlE3QXPVOZ6jYsmiJUf03EZePnmNYtAc1Q3VSUNGJVELTCXlPVtJMSFzFoGrdjDxPLVoSFRMGUfZ7ezm3RHK3cIq/JbaruYiUWTXUNerW0qTiExGhscidENVmmHnpHwo9714Sstw0uqpHgOjCCIlEJkGWgSR3A7JXRCegAyVIhrfgMwe9f0YCTDTOa9/VkUNSo5FhsoQXpvK5guNU3PM1itzwEmihVU4LZvNEgqF+ozohqEq1ixLOeXGj1f95fw9zv3NHAYDI5Lk3c1f96WzlLL9cSE0TWu/CSHe/Q9hGFC6ABqzkE0qkoGKM7su4ILuKulJSKWLSkMRxEO9LnPdG9vTMF1wbNWMQbYqb7gwQVq0lx0IXTnZSKuFwUuDzOVsawYgFSmFrcjhOirc5aRQnVSPlN+to/4mvhaQVTfPX8hyWoYIq9i4NUE52/AQqX25mHxGzUMLKyIbEUVu4eZb1kpPFZ9EpiGEp6rbJEi7AZHapbzr6otWi5XdiMhYKkpQvABZtFAlHrlZpFkERgIhlVYhjVLwkoj0XqSZwDAsbNvuM0ecDz9TLhSCCy9URF+5UqXIDmahyogkeVeS/EjS2Sey75Xv1Q8/6WPKEdXyBqQOKFXadVB2usyR0FAqui+VpauI7Tdbl7mOj0hV/qlbQE66Z1vVubYOegjIaQM+33CVdBY5TcBrU5/lKT+BInca5TFPd+OC/JYm/j/ULykVgK4WHD2iNAcjCpiQqYVMjfos10H1XDdzJkoSqFVOwlBCEV6PQmgsGGGEXQcNe5WZYsZBOko1TzUqJ5y01fm6324npuxvYSDs/crG1xMILQQyi9TDKqPPrkdqOjI8Nvd9gq7ruK6L4zh95ojz4avvp56qQmpz5uTXssHAiCN5NBqltbUV13WPXjr3FBPOQpYtg/q1iNqnVHJGugbSzUqyy5w33bUVmXHA0ME1cvniMmeja0oKC13xScrcXmEoiezZYGdygVf/XAmepjLXcPMk82z1GBtF7K5qvztcBFhFigxS5seSEkQuB8DT1GMh1AIiXHCb1FomPEV+TBARELGcCZJRqaqeyuTDaQO9SVWrpfcr4uuW0mbcfSA8pHARbka9VzMAS3n1w5XKU+9llFRP16hsOykQsQgy1+daOG1IIVRFmxFHOEmklwUtr6Y7jtMvIVe1G2y+o2tPEITQjoBPfOITCCH4n//5H4QQHaR0nxL6SLBboG5dnuypGkg3qC6oqE4uKoRm5p1xIvcYchI655wTuS4UmlALhA9pK1ILTzm9kLn3yFzLEl+SuijVvOtG4BJg+o1QOlFJSV3PLSi+X0GqBcpuUHnk2Vpw6iHbphJhss2KtNJRBBaeep/v6NP0/LW5aZUnT1rVj3s27aqIBOV9c9ViIASYRUizEmFVghkDzUBKgTCjYESRaMobLz3l07DGq7LUcEUuuy8BbhvCblPS3SyB8LjcokG7MOhL+/xoYRhGbxedLleHEUfy1tZWTjrpJFauXEnZYDfXAvXnb3gFcehJaHxVNUpI16twk8yp0UC7k07Tc15xPVckInLqPLkqMS1HJJkjg1ewhWZOE2iX3Dky4XQ5NQmwZDVMPLln1yQ9dV1uUhE106CqzFr3KFvablSLnJvMaRNSVaUZ0ZyUF8onIFPq/U5Sef/9eD5azhyJqGsWpiJrqFSZB0JX55hxpFUJVhnCzapFKJcyK2PTwSpVDShlGpFzOEqhqxh+ZHx7CprjOEgphwzRA5J3A3/605949tlnufHGGwfi47oHN6vSLg89g2h8CVq3Q+aQ+nO7Nh2JmPO6C11JJ5kLsQmZk+oit0CQE4Jejty5DDRSKLW8669bosHsn8Ocy/ou11LmylNdR3mz0weV9pI9iEgfVDZ1pjm3uNnqXH9Bkk5Ojc8tVlKqyIFUZbrg5twAlgrLhccrW1w31eUbpWorJy2MsGshe0hpHkYJMjIWESrPOf0spAipY6FiJdFR/pq+TpQ5GhyFM3D0kFxKyamnnsqNN9542PTXQYP0oHUXNLyIqFsLLVsgvU856Zw0ynvt5787KLeJrzb7j9s9bShS+7ck7/YVS4ph1n/DnMvzZsFAwHOUZM80gtOc8443KYJ7EoGnyO+2qZuTVO9xkioKgabi/zKrNAikUtXNIoQWV45GKZFGFDRVuILTDAi1l1t8MkQnI/Qw0m1DuBlVwpqY3b7I+UTXdb1PEmWOBgHJu4n169fzzW9+kwceeGBAilZ6hUyT2nGkYb1qc9S6A+xDeYnXLo3z6a/tMeb250eCjgwvgWO+CxNOoSddUgYUMnc9bkYROVsP6X2IbB201UCmTiUA2W25+HqS9u9BC+W85rrqRGPlEmAkKgMOTe2fFq7MSXUTmZiVU9mNDkT3ve39WftwJAQk7wH+9V//ldNPP719Y8UhCymVetv8FjS+jGjZDOlduTBcs7JtvSzKzs6Sy2Q5zGAGkEDGZ8Okj0LVRRAbAr6J3kDKnM3eBOkGRHYfJGuU7W03KVPHSaEcg5rqYiOEyi0wwrnwnsi1yUqphJjIRFXoEp2A0CykVU7hLq1DwT4PhUK9FUyjj+QHDx7kzDPP5LHHHiMS6V7nziGBbIvaNLBtJyS3IVJ7ClT6pPJQy1zsnRAylIBQJSTmQfkJULYUQsPoersDKdVC56ZzUn6/6iCT2Q+p/bmchAztbav8EKQZAyOu9jWXnqqfD5UhY9OgeI5qcKF1jCQ7uT5OfZko0xMEJO8hbrrpJhobG7n66qsH+qP7Du1/8EzOK+3kUknD6k+sD76zaFDgZpUnP3NIFayk9ijV3m5Q+fTkCnAMUyXRoJrjSzeDkJ767koWIMedo5JvcvDVdl3XB8URF5C8h7Btm+XLl3PnnXdSXV090B8fYKDgL4TZRmjbrTSgtt05DahBmTzSd2T6RUKeyoEvWoAsWwQlxyriM7j2eUDyXmDVqlXceuut3H777YPx8QEGC9JTLZ2Te1RBTXI3Ir1f2fhOW67FVRZwITwRimcjSxZBfBaEivGkxHEcrKPsKNNTWJbV27eOXpIDnHfeeXz1q1/l5JN7mPgRYORASkg3qr3XUrtVCWs21/vOywIGWMWqzVT5MkjMwpHmgDrihBBHYyKMbpJv3bqVSy+9lEcffXRQwyMBhhCkp3q7p/erxJ3UQdAtlSUXGQuli/G0SHuijGEY/U70gORHiauuuoqJEyfy6U9/ejCnEWAow3PyUt1QZBvIRJmA5EeJlpYWTj75ZB566KF3bOAQIMC7YaAccUfR3w0OQ/Ihmv7UP0gkEvzHf/wHP/zhDwd7KgGGGTRNQ9d1bNvusoR5KGNUkRzgsssu4+WXX+aNN94Y7KkEGGbQdR0hxLAj+qgjuaZp3HTTTVx99dXv6BATIMCRoGkaMhdaGy4YdSQHtSNLdXU1Dz744GBPJcAwg6+2u66LbXfdhONo0B/FVKOS5M3NzXz4wx/myiuv5HOf+xwHDx4c7CkFGEbww2l+66ihjhHX4607uPrqq9E0jRNPPJFoNBp42gP0GH6fQNu2B761WA8xqkJonZHNZlm+fDl33XUXEwZzb9kAwxZ9XbF2FK2fIAihvROhUIj/+q//4pprrhnsqQQYphgOjrhRTXKAD33oQzQ3N/PCCy8M9lQCDEMUOuKGqn0+qtV1H5s3b+byyy/nkUceGdK2VYChCz8j7mgr1gJ1vZ8wa9Ys3vOe9/DHP/5xsKcSYJjCd8Rls9mjSpTpjxBaIMlzaG5u5j3veQ+rVq2ipKRksKcTYBiisLVzbyvWjtKBF0jyd0NRURH//u//zg033DDYUwkwTOHb5z7ZhwoCkhfg8ssvZ/369bz55puDPZUAwxQ+0XubKBNkvPUz/Lz2b33rW0Fee4BeozBRZigUsgQk74QTTjiBsWPH8tBDDw32VAIMYxiGMWQq1gLHWxfYt28f55xzDv/85z+PpqlegFGO3uyxdhSdWmEkd4aZMmUKiUQCXdcxDIN169Yd9Zg33HADjuNw5ZVX9sEMA4xW+PFzwzC61fHlKIXKyCb5unXrqKio6LMxM5kMy5cv5+6772b8+PF9Nm6A0YfuJsocZX83CEJoPYNlWVx//fV897vfHeypBBjm6KtEmV5//oB/Yj9ACMGZZ57JkiVL+PWvf91n45577rnU19fz4osv9tmYAUYnDENVdQ+GI25EqOs1NTVUVVVx8OBBzjjjDH72s59xyimn9MnYb775Jp/61KeCvPYAR40jOeKOslMrjGR1vaqqCoDKykouuOCCPpW8c+bM4cQTT+RPf/pTv7T7CTB6MFgVa8Oe5MlkkpaWlvbHq1evZsGCBX0ytud5/PznP6e2tpYrr7yS973vfQHRAxwVfKIPpH0+7Ns/HThwgAsuuABQXTouueQSzj777D4ZW9M04vE4//Zv/8aJJ57I5s2b+30HjQAjH7quI6Ukm80OyB5rI8ImHwh4nsfJJ5/MLbfcwsyZMwd7OgGGObqyz/08j6PAyLXJBwKapnHjjTfyrW99a7CnEmAEoLBirb9NwIDkPcBJJ51EWVkZq1atGuypBBgBONqKte4iUNd7iL179/KhD32Ixx9//GizkwIEAJQvSUpJNBrtlxBaQPJe4Ac/+AEAX/va1wZ3IgGGPbLZLK+//jrr1q0jk8nwjW9842iGC0jeV0in0yxfvpx77rmHcePGDfZ0AgwD3HPPPbzvfe9j3759rF+/npdeeomNGzeSyWSYN28eS5cu5aSTTuKEE044mo8JSN6XuO+++7jnnnu45ZZbBnsqAYYgPM/j7bffZsOGDWzYsIHVq1dz4MABTj/9dJYuXcrxxx/P4sWLKS4u7stuMAHJ+xJSSs4++2y+853vsHTp0sGeToBBhOd51NTUsG7dOl566SU2bNjAoUOHmDZtGkuWLOH4449n6dKlfPe732XZsmV88pOf7K+pBCTva7z++ut89rOf5eGHHw7y2kcJpJQcOHCA9evXs2HDBl566SX27NlDdXU1S5cuZdmyZSxbtozx48e/Q0JnMhlc1yUajfbX9AKS9weuuOIKFixYwKWXXjrYUwnQx5BSUl9fz0svvdRuR2/bto3KykqWLl3arnZPmjRpqCzyAcn7A42NjZxyyik88sgjJBKJwZ5OgF5CSsnDDz/Mvffey9y5c1m/fj1btmyhqKiIJUuWtEvomTNnDhVCd4WA5ACrVq3iiiuuwHVdPvOZz3D11Vcf9Zi//vWv2bx5M9dff30fzDBAf0NKSSqV4pVXXmmX0G+88QaWZbFnzx4uueQSLrvsMubOnXu0aaYDjYDkrusya9YsHnnkEaqrq1m2bBl33nkn8+bNO+pxTz75ZH79618zY8aMPpptgL5CJpNh06ZN7YR+9dVX0TSNY489tt0xdswxxxAKhaipqeFHP/oR//u//zvY0+4NApI///zzXHfddTz88MMA/PCHPwTok3z0Z555hhtuuIG77rrrqMcK0Hs4jsObb77ZHrp6+eWXsW2b+fPntzvGFi1aRCQS6ZeNDAYZXV7QsNJFQKlavf1xampqmDhxYvvz6upq1qxZ0yfzes973kMikWD16tWceeaZfTJmgHfCcRyampooLy/HdV22bt3aTuiNGzfS2trK7NmzWbZsGZdccgk/+clPSCQSI5HQ3cawIbmvcfg/1sGDB9F1nfLy8sGcVgf8+Mc/5rzzzuO0004L8tr7GJ7nsWvXLu655x5+/etfM3XqVBoaGpg+fTpLlizh/PPP5/rrr6esrGxUE7orDBuS+z/ca6+9xkMPPUQymaSmpoabb765272qq6qq2L17d/vzPXv2tLeO6gtUV1dzwQUX8Ktf/YqvfvWrfTbuaIOUkv3797N+/XrWr1/Pxo0b2bt3L5MmTWLJkiUsX76c2bNnc/311weE7gaGPMlTqRT79+/n0KFD3HjjjbzyyiuccMIJnHjiiVx88cU9aka/bNkytmzZwvbt26mqqmLFihXccccdfTrfr3/96yxbtoyxY8cye/Zsjj322D4df6RBSkldXV27yr1hwwZ27tzJuHHj2p1iX/7yl6murm4PXWWzWVasWBEQvJsY0o63TCbDtddeCyipO3/+fM444wy2bdvGn//8Zx544AE1aA/s9JUrV/K1r30N13X59Kc/zXe+850eXsLh8dOf/pTf/e537b27fvnLX7J48eI+G3+4Q0pJc3Nze+rnhg0b2Lp1K6WlpSxZsqQ9uWTatGlDORY9lDG8vOs+cV9++WUOHjzIcccd12GHlOOOO47vfOc7XHTRRf0y0d6gpaWFeDwOwBlnnMH3vvc9jjvuuEGe1cBj/fr1VFdXE4/H2bhxY3v655tvvkk0GuW4445rTy6ZM2cOuq4P9pRHCoYXybvCzp07Wbt2LY2NjTz33HP853/+J9OmTeurufUpXnvtNb74xS+yatWqUaFWptNpXnvtNdavX88DDzzAxo0bmTlzJosWLWoPXS1YsCBohNm/GJ4k9zwPz/O4/PLLsW2b4447DsdxeO9738tpp53WD1PsO3z1q19l0aJFfPzjHx/sqfQpbNvmjTfe6BCL9jyPBQsWtKvcP/3pT/nwhz/MRz7ykcGe7mjC8CS5j5/97GecffbZbNy4kfLycioqKli4cGFfzq3P0dDQwKmnnsqjjz7arsYPN7iuy+bNmzvEotPpNHPnzm3P6V68eDGxWKyDxtLQ0EBra2uHvIQA/Y7hSXLP89qdMCtXruTNN99k5syZ3Hfffbz//e/n0ksvPaoEmf7GL3/5S7Zt28b3vve9wZ7KEeF5Hjt27Ggn9EsvvURDQwMzZ85sV7mXLFlCSUnJkP2+RzmGZ8abT/CmpiY2bdrEpZdeyoQJE5g6dSqPPvpoh0VgKOJzn/scJ510Etu2bRsy/oOWlhbuuOMOzj333A6x6AMHDjB58mSWLl3KmWeeybe//W3GjBkTELoP8OlPf5oHH3yQyspKXnvttXccl1JyxRVXsHLlSqLRKLfffnufRWaGvCT3sWvXLr7+9a9z22238ec//5nVq1fz1a9+lVNPPbUv59cveOqpp/jJT37CihUrBuXzpZQcOnSoXUKvX7+eZ555hrlz53L66adz/PHHs2zZMiZMmBAQup/w1FNPEY/H+cQnPtElyVeuXMnPfvYzVq5cyZo1a7jiiit6k3I9PNV1yIfT7rnnHtauXUs0GuVrX/vasKrfvvjii7nsssv4wAc+0K+fI6WksbGxQyx627ZtlJWVdWh04Loul19+Oc8++2xA7AHCjh07OPfcc7sk+ec//3lOO+20dift7NmzeeKJJxg/fnxPPmJ4quuQT2m98MILOfPMM9udWENdVS/ET37yEy688EJOOeWUPgsjSSlJJpMdCL1582bi8Xh7csnFF1/MzJkzu4xF/+Mf/wgIPkTQVfFUTU1NT0neJYYFyQtR6KUeLgQHmDRpEueeey6/+c1v+NKXvtTj90spSafTvPrqq+110a+//jqhUKg9Fv2f//mfzJ8/v9uNDkpLS3s8jwDDD8OO5MMZV111FcuXL+cjH/kIY8aMOex5Ukq+8Y1v8LGPfYxXXnmFDRs28OqrrwKwYMECli1bxhVXXMHChQt7lLsf4Mg4UuegXbt2cfnll9PY2Ijrutxwww2cc845R/25/Vo8JaUcyNuox1133SU/9alPyWQy2X5ramqSa9eulbfccov8whe+IE844QQ5duxYuXTpUnnTTTfJp59+Wra2tkrP8wZ7+iMajuPIadOmybfffltmMhm5cOFCuWnTpg7nfPazn5W/+MUvpJRSbtq0SU6ePLnb42/fvl3Onz+/y2MPPvigPPvss6XnefL555+Xy5Yt680ldMm7QJJ3A9dddx2/+c1v2qXvD37wg16v3hdddBE/+9nP+NGPftTeCbS5uZlZs2a129A33HADhmHw/ve/ny9+8YuEw+G+vJwAh8GLL77IjBkz2kOdH/vYx7j//vs7tAcTQtDc3AyosO6ECRO6NfbHP/5xnnjiCWpra6muruZ73/te+26mX/jCFzjnnHNYuXIlM2bMIBqNctttt/XZdQ0L7/pg47rrriMej/P1r3+9T8a75557uO+++7jkkktYunQp5eXlXTrA/E3qAwwM7r77blatWsVvf/tbAP74xz+yZs0abr755vZz9u3bx5lnnklDQwPJZJJHH32UJUuWDNaUOyPYn3yo4MILL+QPf/gDZ599NhUVFYf1cAcEH3q48847+eQnP8mePXtYuXIll112WXtp8VBFQPJu4uabb2bhwoV8+tOfpqGhYbCnM2qxatUqZs+ezYwZM7jhhhu6POeuu+5i3rx5zJ8/n0suuaTbY3fH+fW73/2Oiy++GIATTzyRdDpNbW1tL65kAHE4Y72fbkMWH/jAB+T8+fPfcbvvvvvk/v37peM40nVd+e1vf1t+6lOfGuzpjkp0xzG2efNmuWjRIllfXy+llPLAgQPdHt+2bTl16lS5bdu29vFfe+21DuecffbZ8rbbbpNSSvn666/L8ePHDyWHaJe8C0jeQ7ybhzRA/+K5556TZ555ZvvzH/zgB/IHP/hBh3O+8Y1vyN/85je9/ox//OMfcubMmXLatGnyv//7v6WUUl5zzTXy/vvvl1Iqj/pJJ50kFy5cKI899lj58MMP9/qz+gGBd7232LdvX3vm0b333suCBQsGeUajE91pqb1582YATj75ZFzX5brrruPss8/u9mecc84574icFO6MM2/ePJ599tneTH/QENjk3cA3v/lNjjnmGBYuXMjjjz/O//t//2+wpzSk0R27GeBvf/sbQgjWrVvXZ5/tOA5btmzhiSee4M477+Szn/0sjY2NfTb+cEQgybuBP/7xj4M9hWED13X58pe/3GErqvPOO+8dW1G1tLTwv//7v5xwwgndHrs7jrHq6mpOOOEETNNk6tSpzJo1iy1btrBs2bKju7BhjECSB+hTFCaUhEKh9oSSzrjmmmu46qqrepToU9hS22/LfN5553U458Mf/jBPPPEEALW1tWzevHnI1PEPFgKSB+hTHK6aqhAbNmxg9+7dfOhDH+rR2IZhcPPNN3PWWWcxd+5cLr74YubPn8+1117b3p77rLPOory8nHnz5vG+972PH//4x0Nql53BQKCuBxhQeJ7HlVdeye23396r9x/JMSaE4KabbuKmm246mmmOKASSfBTiSI6xm266iXnz5rFw4UI+8IEPsHPnzm6PfSS7uaWlhddee43TTjuNKVOm8MILL3Deeef1qfMtQCccLrbWT7cAg4zuJJT885//lMlkUkop5S9+8Qt58cUXd3v87iSUFOLUU0+Va9eu7d3FBOiMLnkXSPJRhu44xt73vvcRjUYBWL58OXv27On2+N2xmwMMLAKbfJShp3u0/+53v+ODH/xgjz7jSHZzIXxPeID+QyDJAxwWf/rTn1i3bh3f+MY3BnsqfQLZqax69erVVFdX87Wvfa3L4yMFAcmHKI7kHMtkMnz0ox9lxowZnHDCCezYsaNb43a3zdCjjz7K97//fR544IFh32Jq8+bN7dl1juO0v75kyRKuuOIKnn/+eYCR29TycMZ6cBu8G6ADbwPTgBDwMjCv0zlfAm7JPf4Y8Jdujm0A24CpBWPP73TOcbnPnznY30Uvv79K4KSC5xcDLxU8L+p0/ttAYrDn3V+3QJIPTRwPbJVSbpNSZoEVwPmdzjkf+H3u8d3AB0Q3RJGU0gG+AjwMvAHcJaXcJIS4Xgjhp4/9GIgDfxVCbBRCDFmPmRBCF0Jona5dAN/OHY8BLwKOEOI/hRDrgUeFEPMK3pMC5g7oxAcQgeNtaKIK2F3wfA/QOcm7/RwppSOEaALKgSN2MJBSrgRWdnrt2oLHp/du2n0LIYSQOVGbI6QApP8a6olbcH5ESpkCTgdOFUK8AjwPXAeYqIVrKXAN8GngZ8BO4C3UwvriAFzWgCMgeYAhBSGEBSwEWqSUb/qv54gtO52rAeflzn8/UCyE+CrQDLwC3Cal/G3u3INAo5RSCiGeyr1vBorkL6JI3mFhGSkISD40UQMU7vlbnXutq3P2CCEMoBioG5jp9Q2EEDqKv54Q4pfAEtR/sgVoFEKsBFZIKZuEEAuAs4Ai4Pc5U8YTQnwJiAHnAqegTJGbgb8C0ws+7lFgZu7xHsAG/FarzwIfgfbFZEQhsMmHJtYCM4UQU4UQIZRjrbNd/ABwee7xRcA/h8sfNGdH3w20An4N6knAA1LKxVLKU4GfA5cCHxVCJIB/R0nyZuCzQgh/c/p1KAndADwOPAVcCLyOciD6eAkluQH2A9mC5xuBMiHEiNxSJiD5EEQ3nWO/A8qFEFuBK4Grux5t8CAU9Jxa3Y6cHZ0Bvi2l9Hf/W0VOsuZs69XAncDHgbOBMEoazwA+DBybe98zQFnucQpIorSBLeQktxCiKvd8Xm7sVuA1YKMQwso9bwZGZsufwXbvB7fReQP+DaV2+8/PAV7LPTZz97OAg8C1KJLeClwBLCh43yQUsRfknv8ZuDj3eAVKov8StRCcA0S6mMtVgAecN9jfS3/cBnpzhQCjCEKIWcAXUBLybSnlF33HlhDiVOAGKeWJuXNLgR1SyuJOXvVG4PvAeCnllQVjV6EWAA9l3tSgiNwEfEZKuTc3ZquU0j7M/AypIhOVQMPhzhvuCBxvAfoFQogw8EVgE8p/8DZ0cGy9BcSEEEVSymYpZYMQIiWEmCNzXnUhxMeBF4B/AD8SQvwY5TB7D3Av8HMppSuEeA44KKW8vuDzNans9MN6zKUyi5BSHny384Y7Aps8QH8hA1wC1ANrpJS7Ox0/lDu2qOC1TSgPO0KIs1EOxd9KKV8HPoPKC0ij4t6/kipRyB/rmNz7zBxZ27c16S5xRyLBYeD3QgswClCgkn8XGAOMQ6nTN0opdxUc/xVKjf9R7n3fB76FCmm1AvcAf5IqweXdPm8KMEZKubb/rmr4IiB5gH5HTip/BLhVSvlswetfAE6RUl6Se14CxKWUhy1gz8XWvZEqdfsDgU0eoF+Qi22fhkq/XYqymZ/tZPe+jIp5z5JSbpZSNgKNuffr0DFttavnBZ83Iu3pvkBA8gD9BQ8VshLAP3O3znbvVtR/8PdCiDOkileTO69LMh8OAcEPj0BdDxBghCPwrgfoV3SV8XaYc0Zox4bBRyDJAwQY4QgkeYAAIxwByQMEGOEISB4gwAhHQPIAAUY4ApIHCDDCEZA8QIARjoDkAQKMcPz/+ORg611qOnMAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x216 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Trajectories in space-depth\n",
    "plot_2D_space_depth(t_span, trajectory, yn, len(X))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3c2bf699",
   "metadata": {
    "papermill": {
     "duration": null,
     "end_time": null,
     "exception": null,
     "start_time": null,
     "status": "pending"
    },
    "tags": []
   },
   "source": [
    "## Galerkin-Style Neural ODE"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "391a9a25",
   "metadata": {
    "papermill": {
     "duration": null,
     "end_time": null,
     "exception": null,
     "start_time": null,
     "status": "pending"
    },
    "tags": []
   },
   "source": [
    "Galerkin-style Neural ODEs proposed in [Massaroli S., Poli M. et al., 2020](https://arxiv.org/abs/2002.08071) make the weights of the neural ODE to be *depth-varying*, i.e. $\\theta=\\theta(s)$ obtaining a model of type\n",
    "\n",
    "$$\n",
    "    \\left\\{\n",
    "    \\begin{aligned}\n",
    "        \\dot{z}(t) &= f(z(t), \\theta(t))\\\\\n",
    "        z(0) &= x\\\\\n",
    "        \\hat y & = z(1)\n",
    "    \\end{aligned}\n",
    "    \\right. \\quad t\\in[0,1]\n",
    "$$\n",
    "\n",
    "where the depth evolution of $\\theta(t)$ is parametrized by a trucated eigenfunction expasion, usually an orthogonal basis of some functional space, i.e.\n",
    "\n",
    "$$\n",
    "    \\forall i \\quad \\theta_i(t) = \\sum_{j=0}^{m}\\gamma_j\\odot\\psi_j(t)\n",
    "$$\n",
    "\n",
    "The model is then trained by optimizing for the eigenvalues $\\gamma_j$. Note that if $\\theta\\in \\mathbb{R}^d$ there will be $d\\times m$ final model's parameters. In this tutorial, we use a 10th-order polynomial expansion to model $\\theta(t)$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "522e1bef",
   "metadata": {
    "papermill": {
     "duration": null,
     "end_time": null,
     "exception": null,
     "start_time": null,
     "status": "pending"
    },
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Your vector field callable (nn.Module) should have both time `t` and state `x` as arguments, we've wrapped it for you.\n"
     ]
    }
   ],
   "source": [
    "# vector field parametrized by a NN with \"GalLinear\" layer\n",
    "# notice how DepthCat is still used since Galerkin layers make use of `t` (though in a different way compared to concatenation)\n",
    "f = nn.Sequential(DepthCat(1), \n",
    "                  GalLinear(2, 32, expfunc=Fourier(5)),\n",
    "                  nn.Tanh(),\n",
    "                  nn.Linear(32, 2))\n",
    "\n",
    "t_span = torch.linspace(0, 1, 2)\n",
    "\n",
    "# Neural ODE\n",
    "model = NeuralODE(f, sensitivity='interpolated_adjoint', solver='tsit5', atol=1e-3, rtol=1e-3).to(device)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "6340e53d",
   "metadata": {
    "papermill": {
     "duration": null,
     "end_time": null,
     "exception": null,
     "start_time": null,
     "status": "pending"
    },
    "tags": []
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "GPU available: True, used: False\n",
      "TPU available: False, using: 0 TPU cores\n",
      "/home/michael/.cache/pypoetry/virtualenvs/torchdyn-voYSR01p-py3.8/lib/python3.8/site-packages/pytorch_lightning/utilities/distributed.py:69: UserWarning: GPU available but not used. Set the gpus flag in your trainer `Trainer(gpus=1)` or script `--gpus=1`.\n",
      "  warnings.warn(*args, **kwargs)\n",
      "\n",
      "  | Name  | Type      | Params\n",
      "------------------------------------\n",
      "0 | model | NeuralODE | 1.0 K \n",
      "------------------------------------\n",
      "1.0 K     Trainable params\n",
      "0         Non-trainable params\n",
      "1.0 K     Total params\n",
      "0.004     Total estimated model params size (MB)\n",
      "/home/michael/.cache/pypoetry/virtualenvs/torchdyn-voYSR01p-py3.8/lib/python3.8/site-packages/pytorch_lightning/utilities/distributed.py:69: UserWarning: The dataloader, train dataloader, does not have many workers which may be a bottleneck. Consider increasing the value of the `num_workers` argument` (try 48 which is the number of cpus on this machine) in the `DataLoader` init to improve performance.\n",
      "  warnings.warn(*args, **kwargs)\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "5bfc5812992240c19e72611acedfd77e",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Training: 0it [00:00, ?it/s]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/michael/.cache/pypoetry/virtualenvs/torchdyn-voYSR01p-py3.8/lib/python3.8/site-packages/pytorch_lightning/utilities/distributed.py:69: UserWarning: Detected KeyboardInterrupt, attempting graceful shutdown...\n",
      "  warnings.warn(*args, **kwargs)\n"
     ]
    }
   ],
   "source": [
    "# train the Neural ODE\n",
    "learn = Learner(t_span, model)\n",
    "if dry_run: trainer = pl.Trainer(min_epochs=1, max_epochs=1)\n",
    "else: trainer = pl.Trainer(min_epochs=100, max_epochs=100, progress_bar_refresh_rate=1)\n",
    "trainer.fit(learn)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f459796d",
   "metadata": {
    "papermill": {
     "duration": null,
     "end_time": null,
     "exception": null,
     "start_time": null,
     "status": "pending"
    },
    "tags": []
   },
   "source": [
    "**Plot**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "0c1bff2c",
   "metadata": {
    "papermill": {
     "duration": null,
     "end_time": null,
     "exception": null,
     "start_time": null,
     "status": "pending"
    },
    "tags": []
   },
   "outputs": [],
   "source": [
    "# Important: notice how we are passing `t_eval` to the plot below? `interpolated_adjoint` Neural ODEs save all solution points evaluated in the forward pass, even those\n",
    "# outside of a given `t_span`. This is to ensure the interpolation in the \"backward pass\" is more accurate. This also means that `len(traj)` will be > 100!\n",
    "t_span = torch.linspace(0,1,100)\n",
    "t_eval, trajectory = model(X_train.cpu(), t_span)\n",
    "trajectory = trajectory.detach()\n",
    "t_eval = t_eval.detach()\n",
    "# if you wish to recover only points at `t_span` with `interpolated_adjoint` Neural ODEs, use their `.trajectory` method"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "a8e0cb34",
   "metadata": {
    "papermill": {
     "duration": null,
     "end_time": null,
     "exception": null,
     "start_time": null,
     "status": "pending"
    },
    "scrolled": true,
    "tags": []
   },
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 576x144 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Trajectories in the depth domain\n",
    "plot_2D_depth_trajectory(t_eval, trajectory, yn, len(X))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "122a456c",
   "metadata": {
    "papermill": {
     "duration": null,
     "end_time": null,
     "exception": null,
     "start_time": null,
     "status": "pending"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 216x216 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Trajectories in the state-space\n",
    "plot_2D_state_space(trajectory, yn, len(X))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "a25e0693",
   "metadata": {
    "papermill": {
     "duration": null,
     "end_time": null,
     "exception": null,
     "start_time": null,
     "status": "pending"
    },
    "scrolled": true,
    "tags": []
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/michael/.cache/pypoetry/virtualenvs/torchdyn-voYSR01p-py3.8/lib/python3.8/site-packages/mpl_toolkits/mplot3d/proj3d.py:136: VisibleDeprecationWarning: Creating an ndarray from ragged nested sequences (which is a list-or-tuple of lists-or-tuples-or ndarrays with different lengths or shapes) is deprecated. If you meant to do this, you must specify 'dtype=object' when creating the ndarray\n",
      "  return np.array([xs, ys, zs, np.ones_like(xs)])\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x216 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Trajectories in space-depth\n",
    "plot_2D_space_depth(t_eval, trajectory, yn, len(X));"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e5eb8270",
   "metadata": {
    "papermill": {
     "duration": null,
     "end_time": null,
     "exception": null,
     "start_time": null,
     "status": "pending"
    },
    "tags": []
   },
   "source": [
    "## Data-Controlled Neural ODE"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1fae5c8f",
   "metadata": {
    "papermill": {
     "duration": null,
     "end_time": null,
     "exception": null,
     "start_time": null,
     "status": "pending"
    },
    "tags": []
   },
   "source": [
    "Data-controlled neural ODEs, also introduced in [Massaroli S., Poli M. et al., 2020](https://arxiv.org/abs/2002.08071) consist in feeding to the vector field the input data $x$ (the initial condition of the ODE), leading to\n",
    "\n",
    "$$ \\left\\{\n",
    "    \\begin{aligned}\n",
    "        \\dot{z}(s) &= f(z(s), x, \\theta)\\\\\n",
    "        z(0) &= x\\\\\n",
    "        \\hat y & = z(1)\n",
    "    \\end{aligned}\n",
    "    \\right. \\quad s\\in[0,1]\n",
    "$$\n",
    "\n",
    "In this way, the Neural ODE learns a family of vector fields rather than a single one. \n",
    "\n",
    "In practice, we concatenate $x$ to $h$ and simply feed $[h, x]$ to $f$, which should indeed be defined to accomodate the extra $dim(x)$ dimensions. Data-control inputs can be defined at any point in `f` via use of `DataControl`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "a522c5ab",
   "metadata": {
    "papermill": {
     "duration": null,
     "end_time": null,
     "exception": null,
     "start_time": null,
     "status": "pending"
    },
    "tags": []
   },
   "outputs": [],
   "source": [
    "# vector field parametrized by a NN which takes as input [h, x]\n",
    "f = nn.Sequential(DataControl(),\n",
    "                  nn.Linear(2+2, 64),\n",
    "                  nn.Tanh(),\n",
    "                  nn.Linear(64, 2))\n",
    "\n",
    "t_span = torch.linspace(0, 1, 2)\n",
    "\n",
    "# Neural ODE\n",
    "model = NeuralODE(f, sensitivity='interpolated_adjoint', solver='tsit5', atol=1e-3, rtol=1e-3).to(device)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "2768eea0",
   "metadata": {
    "papermill": {
     "duration": null,
     "end_time": null,
     "exception": null,
     "start_time": null,
     "status": "pending"
    },
    "tags": []
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "GPU available: True, used: False\n",
      "TPU available: False, using: 0 TPU cores\n",
      "/home/michael/.cache/pypoetry/virtualenvs/torchdyn-voYSR01p-py3.8/lib/python3.8/site-packages/pytorch_lightning/utilities/distributed.py:69: UserWarning: GPU available but not used. Set the gpus flag in your trainer `Trainer(gpus=1)` or script `--gpus=1`.\n",
      "  warnings.warn(*args, **kwargs)\n",
      "\n",
      "  | Name  | Type      | Params\n",
      "------------------------------------\n",
      "0 | model | NeuralODE | 450   \n",
      "------------------------------------\n",
      "450       Trainable params\n",
      "0         Non-trainable params\n",
      "450       Total params\n",
      "0.002     Total estimated model params size (MB)\n",
      "/home/michael/.cache/pypoetry/virtualenvs/torchdyn-voYSR01p-py3.8/lib/python3.8/site-packages/pytorch_lightning/utilities/distributed.py:69: UserWarning: The dataloader, train dataloader, does not have many workers which may be a bottleneck. Consider increasing the value of the `num_workers` argument` (try 48 which is the number of cpus on this machine) in the `DataLoader` init to improve performance.\n",
      "  warnings.warn(*args, **kwargs)\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "16d94d3313a8448f9e964a43386506fa",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Training: 0it [00:00, ?it/s]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "learn = Learner(t_span, model)\n",
    "if dry_run: trainer = pl.Trainer(min_epochs=1, max_epochs=1)\n",
    "else: trainer = pl.Trainer(min_epochs=150, max_epochs=250)\n",
    "trainer.fit(learn)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7c7b873a",
   "metadata": {
    "papermill": {
     "duration": null,
     "end_time": null,
     "exception": null,
     "start_time": null,
     "status": "pending"
    },
    "tags": []
   },
   "source": [
    "**Plots**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "5a0cf018",
   "metadata": {
    "papermill": {
     "duration": null,
     "end_time": null,
     "exception": null,
     "start_time": null,
     "status": "pending"
    },
    "tags": []
   },
   "outputs": [],
   "source": [
    "# let us try the `.trajectory method` here\n",
    "t_span = torch.linspace(0,1,100)\n",
    "trajectory = model.trajectory(X_train.cpu(), t_span)\n",
    "trajectory = trajectory.detach()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "f417174c",
   "metadata": {
    "papermill": {
     "duration": null,
     "end_time": null,
     "exception": null,
     "start_time": null,
     "status": "pending"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
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RNrR7werbDx9WYh2G1kPQx8xDt1NnPu9Jd+h9Q59rt78p6fZDwrdQvO3bSuzGYyX11dXdgj4zKLa2YDbT/TXNlZ/KhegLbi10LZx/UpvXvPABHfs6OwFs05N7QD33ESpyCzoRTnKYfHSbhtrDSj7LOw2VtzN1osMot6U9AP4ATF6nIXZxWvK2fhSaszA/r8fzOT8/Oqyeu8sd8NxEPX9f6/5TA+35ntzbnazSzz3vrdwO1Kt3+3N6nYg8BayjYZI2pXTf9V1RwY2EzU345CfVa3/ve+Ho0Qtvu7LS17fX9e6wuYXLrd2sed5G7kbqJqaD3nu3BjdGzObtW9jewvAm1jNin0z6PL/l+LsONjZ0Lr2J+ZpGH28ava2sXNlnVoi+4OZHN4ezn1cx3QsfhvOPa+6bGco1ppQfoWH5OnvvQcPj9aEsjrtdPfTglGyZQUzah95PdNBMOJRV8nfq/1PUsbLrx5Tc2zxe1vlM4hOtm/dTDfdXa5p7F6cef9zRLnpx3ufgAcj5fZfdjzRXIyKdB0TX3W0DVzgN49rhT6eULlDIVFCwG8ePw2/8ho54/fjHLxySh5cOihmG2MfjvoHNsuJ9uQZ+CPPazRBIabe63sLxFvIfj5XUrXnOMILQND2xW7vbGHuSt5C/3Ya6gMtFIfqCmxPNNpx5EJ7+FTjxcdh4AtpzaBlch4rjPNqdLg+O8SHn26caOh/luvWQ+0/GHWBHxfauymVsIzUCwmENzbucM29OweYZnUC3qG8f637rFfX0q0zuIYfkQT31uJ3/ZjFdbJXQJeTHW6DN+oGGRZ2+n2Rx31jXVobaFNygaFv4/Oc1HG8jXi/UNGY00jz7oUN6fxhSN6/dSNw60Vnu23LtQ6W8eerDXPvwMXvdeNyH3KfTntwtPD9slLO52YfhjdiN3G3/dgwzHizsb4bKlaAQfcHNg9k6PP8ROPZeOHO/lsG1GygZmpjOyL3KpF7p/WpFG9iMjigJh6Bh8W6ePWOU8CW3na0OZy9/pSfl2fMqqOu2ct7cqfEwuk2V9cHK4Cw0P84ldhG63M0uJVQ5n2/tlu47dvoenORSvJEaDG6aB92saCTCmTI/e/v7Ewn4gIgk4N/nEdMFtzjOn4ePflRD8r/5myqsuxDW1jS/vbLST4EzAl4m96F3bI1qhv3noSf4Yd9589qHuXxT3xupW6ndcChNSppjn8/7/dnxjeTtGAZ77dDYsONbCP9KsG+vBAUFL4uFUv634Ln3wZlPweZzuTa9pc+3Dzx3P8pd5TxUq7kpzRElbBf0NTEq6UqA6qCG2esDmncPB7XxjZHw5kkNrbebWeQuWUB3ULc3gjdlvh/nZOA8e/qdNsjpZmpQdDtZNZ9H1UqNKvvzjHk/1f1UUyV1qXPIf1WjBWGq26d5FgfuS/zJlNIxEbkT+E0R+XxK6SP2pIh8L/C9APfcc8/1WmPBNUbX6aCYX/91rW9/6KELD4oB9dgPHVKSNWIflrbZABl7bhiSH/aRN49/SLhW0z5sP2siOSN0O4bdzPNuW22da6Q8jAAMhXQWTTCRnukChp+H6QSG+X4onfEKbjXEqGK2594Hz70fzj2iA2PYoq9xz53pGPXtYH2AWMPkQA6fH8ptYgeFrnRKnKNRbkazmhXvq328rzsPO1sQN6HZyS5Bzpf7FTUI3CR3phsr2UsNkifVpaSh9zhTMV63peTe7bAYSyuh99Ilk7gfZW993D9XrWW1f9UbDs35LNxrVeEf9l8b3JTSsfz3uIi8C/ha4COD538C+AmA++67r9QI3kTY3NRe8r/8y9q45plnLrzteKwiupWV3W1lzROfTHovfhhmNwK2ML6p5YfiOfOyh+Vww5nw5rUPR8naftpWPfblqXNG6t3gVLe/Fl0YKvKHzw+J3N6fhetFbpHpdUWle4ujbeDcF+HYu1VMd+7z0JwGdlDPPbGob2ecvfZM9m4CoxX1sKtMiljhK7nv/Kgvg7NWsyGrZ2KXyX1Tc+Jdp958qLK3nqMCfqy58WpVQ/8u6LpS1LK5uAmzDW26E3dUQY9nkbuvD2evfyWH9Ue5De5qNhxW8r5z/TySif0cbG/0qnzMVcj73mcQkRXApZTW8/0/D/yz67ysgmuErlNV/Pvep177pz518ZrwtbV+AtywZax57UbCyyQ9JPRhX3nQbWYzvT9sWGMEbOK7YenbsLNdSiqcs9fbY+bB2zqGgr1hL/vhMBt7fujRm+p/OK1u2du/lcR4RaV7K6HZ1razR98DJz8K609CZ2K6lj7fvsLCe6/rHMqeqBder6kgTXJe29rSYgm6SW5IM1Ky9RO0HS3qGbebWfmez25GGjofrfaee1jpyd4Mg3ZHm94063rrtnPOPeX8ep272eX9uVrTAcFIPRN6NWUxnEa8ev3NedjezA1y8n6dy9GACg335657+7Nhzl3Au0SvYgH42ZTS+6/vkgquJjY2VBn/S7+kBH/06O589BDew5EjqpQ3ohv2eDfF+lAIZ2r34TZGlMMwuXntRrwWMjflvXW9G4/7/LuJ9Cwnbq9dDskPidvIfHiMYaOc4VAaK7kbbmvv115jRsIw1WBNfS4XNxLRF9zs2DkLz39YB8acvR82n4VogRwT0wU0JD8Cxuo5h3HOsU90CEwY9c1tkug2Lteq+1wP70P+Wykpdo2W3HVz9bgFfW3IzWtsNGxYVQKuDun+ZA7NBuy8kEPx25pvZ66d7XwebuPzsBnv+1y97ctPc1RgpGI/8XpLUQfYNEdVVNjlznfiegMgTPMx6kzuGUI2avYXUkpPAG+/3usouHpoW/jiFzXX/gu/AA8/rDnrC8E60pnnbAQn0ovohk1rLBS+FwEaQcaoXvuwph12N6lZFs4Na+OH3vmwTt6ObWsZdsYzgh+SOuwmdiurW26Lu3yz92Mja21d9vdWmUdfVLo3I1KC80fh+ffDc78JZx9SwsTaziZY9JRfAWoNjyefQ+WrSvCL5jI14Onb00oOyefwuPWKdza/faY97ZnnJjTk2nkLld+mf0drStKS+9A36zA7rsSe5hp9SLklFpmk3ZoOm/FVDsNnUg+23rGK/MRlgvbazCeuaySh3c4h/sGaRkc05+9snO3ws4xqBCz+7+hr7gsKri5OnIDf+R312j/0ITh16sLbiuhQFuvbPgxPD9vAGlEut4wdiu4sRz5UsQ/Fa9CL6IZtbIc57+VZ73Z/mG8f3h8SrR13mGsf1tIPS/aMsIeK+uGQm2H73GHe3h63jnwi+tldCW4Uor+oShcoSt0bBW0D578AT79bW8+e/SK0lm83ovJo85qJ3g/jXDo20bp1fwDqafaAR9q1ztXKa67OBJrb1OKzqM0DSQl9vq616hG0TW322seHNZdfH1BiFRPr7cDsFLTHsio+58OTAKLRAZdTBItQ/Fr21icsetJLTjqmmGvlnRJ5l0voiANiHyuxu3FWzxuzp3470MclP97lnvyx1fWVOvqCq4StLbj/fh3t+t73whNPXHj6G/Rz281DN4/Ycu3LxGv7svay9ndYi75crga7CdHy93Z/aCQMSXlYsz702g1DT3rotQ9r74d6gKG3Dv3xhlEDM1SGtfz2/ux5+zyGBoNtt9zA55XihiD6l1Pp5ueKUne/YrYBL/yuDos5+bEckj+H1rcPOr0xRQV1lYbfpVaSrnPOPYyUON1Iw9KWd7dJcJUpaKbq+eN1/82mknVrTbC9kvBkFfzh3Ko2t9GSUfbS16HLpXMxgkTNv0uujVdNWc7T5wY1PkcNCPp2kmTSjdn4aJTsEVXFW628BBX3uZyKcCMWNfBmGCTQUrzhzebY56ukfR4uq/b3oRiv4MZA02gI/r3v1aY1X/jCxUV0IajXPlS6w25v1sjKSHHoMdu8dSM+I9adnd2heNvXMCRvZG+ku9xwZphbtwjAUKk/JH9bn8HWb1PlrC7fhIKWjx/W55u4zgwD28+wV/5wrcNjDLcd5v5v+vK6otK9AZESrD8PL7wfjr4fzjykzWQWIXlDBYxZtJ4NI/V+g9WKr/b/D2MlTkkaundOyROvxBgmfT6824ad05kIW7CWsKPDEG7Lk+BGQC5lo+296m6nJ+DUaRpAUC/dh/x3RY/txuASi5H0qdGWuDRqMFjNOx7E5LltJmmyYZBb7iY7szsVADbbPaGTBmQuLMrwFk1ycm8AV2eiX3IxCgpeBinpjPb3vx/e+U548EFYX7+wiA5URGfT1syLjXF33fowD2416vb4sOwN+vayw9avRnTDiW7DITPLZDkMmZuhMKyPt/0NBXomrjMxnu1vGBWw92CEP3yfw8qAYd59WCZnn9Fwm2WF/YUI3455Jdj3RE9R6d4YaOdw6rPwzK/C6d+DM5+HeBpVyQ9zxZlgyWH3qlIPfDQGJjpn3WeP3NTjMWaSl0y8vjcGpNZQereVS9caFip0v6LeuqxAPVZvWkJ/1Ukb+a/1uzfGjtmznmSSz01usLM4E3Xc1vC+z41swghcJl/pcke7uUYIFvB9eoGUjYusIrLP6SVkblUBWV/gcjTDvHnz7rstvW+Pje/Qz6ugYAkxwlNPqYDuV38VPvMZOHPm4sQ+nWrp25DEhiRonmrb9mHoC7WabfKgRiPi5Zy4EaPdlr1gO57BTmkro1v2yofk2TS7SdXq1If59mWR3NDLXn7fw/e33HlvuB87vv21fPzQUDDDwLaz41vE43Kx74m+qHT3KVKC2Vl4/oPw7HvgzGc0JM8mGpI3COq15xI4GUGdCaua0peR5TI5EXAxi8mcvt5lrzesspjz3m7n3H7uLOezdz46mJvXGPHmfZDFaWmmangcffc8iwsGzXO7SnPzi8bTHWCNd3J/e6t39xYiz2TbbuvwGhtAY3X7lmqg0+fSXp75OHvmAzGhRQCMvNuNQVRgcDVL+X3YcVN2UwrRF6A/5S99SUPx7363huVPn35pfnqIyUSJfZhHNgxD8kOlOPSkbGRoHrR56pZrHyrjh+Q4JPjhQBr7a4TcNLvD57auoajNQvV13W87mewm1GEI37z8oQe+Vye7odExbIZjRspwuyGR2/sdRiqWP4PlQTbDJjyXi31P9AX7CO0czn4Onnw3nP6IToTrTqJCuiFCvlVoSH4yIPZcVhZWs+crSqptBN9pKFu8vq5aUWK3lrTtOnRnIAUgsRjksmgqM1HytJI6XA71Sw7F51B+17FoLpMalIi9evwhq+TdCEZ5uE0Y5S50WTcAuVZ+U2fJx3zFETJJZ42BdbkzcZ2RuTXDMYHggrg7rQQwzzwNIiEpe/xG5HE5X7+0H4DRHaiRVXCroWl0Nvt73qN94x95RCe+XUxAF4KWvlku2khu6D0PQ+7Qk+pymN6U68PBLbb9cujeBHTDqMByw5phz3roG9dYKdzw/tCzHk6w20s7AH0DnuXQ+nL5m617WAFg73eZpPcKwQ+9/WGEwN7jcq0+9OmDW0KMV3CdkBJsHocXP6TtZk/cDzvHgA1eWroVUCFdDsuHcb6NVIHuV7NALAvT2qweJ4fZ6xwCl3H2fPMwmXaThadq/eJlmo2ATOyWL5egxI6oUdJtadg8Nkp+knPdYtv7TODZM/eruV5+rJEH5zKhNtrXfm6kHvUYll+vD+Z0wyDM7mp6tXzsw+up07K5bmOJyM3Tt1RC3E3cMRO57csgFrGwq1LWLCxKEwtudqSkrWU/9jHNsX/kI+q9r69fnNittnxY6z30YId57+Gx7HnDsPRsWHc+rI+37UxAZ16w5d6H4jZbw1CEtyw5sW3ath9qY0K4YQh8Wcw2LHEbkvHwfQzL2pYb8gxJfPmzsv0P0xRDkh+W0i0r/ofHshn2RvIp3TrldQWvFpoteOGT2pHu1Efh/BeB8+wOx4OSSy5fs4ExYaQKecledpgATj32DrSXvNfH6io/nxvWmDcbszcrksV1WWlvJW8miJOsUCdfXaxZTewg7WRPHhZlbYvxs1Pwa7qvMO09cOd6km3WIZ3tCd2Zkt3a0K5m4yXXwi/I3Ii8y4NuzutHlbJRE+fsEvotDIDYRwUWnrzpBRi4FlZhMLjyWtohkY2BOUjum1+0eDclrK3shz+sM9ofeACOHVOyv1iI18rPrEe8Pbbc1W3ZG7Xnl4l/WHZm3uiwbGyoiB967kMSHYrjLApgE+OWVfHL6vbhX9tuWQg3JFrbxmCe+rKXPtx26NXba5YFdZbSGIrvbFvYHYWw9zqMXFjjIHufJkq01ESMGmm5EhSiv9XRzuHcY/Dsu+H4h+HM56A7Acz22Njy5iMW+fbxCiqiy4K0lIldJHOVqBEwsiEzmTitVWxcZ1GK5kZK5OGIhvYr84xXgJBrzTs1Rrrj0HYg8xzOzl6tz4NffBb1+bFGC8ihdOdV1LZwEbKnHPP7W+gBJjm9kLvPic/Gg3ne3YDIM8lb5CBFXacJ/RbePP1z5GMboUv+bJ1Djaf8eBoSefboF+18B9+LywaNC2q4LEoPC25kpKQh9wcegN/+bR3j+sUvwsmTfSe4C8FK0MxjH4rChvtf9m73IrMhaQ37u8NuT9iIbkjudt/2PQxXw26SH86Nhz6sbp76shBw+J6GBsRyTn3ZW182XC4UsrfX2v8thWHvc/mzGva1Xw6/D2fVD7UEQ1JPaffzZnjc9GK8gquMtoFzX4Jj/wVe/B048zC0x4EL9awUFsNiFv3kVzSXHVbyL9zatsKiSY15yeSrSOwgnddcvPNoaVutofP6wCB8nge2kFQ012zC9omeSGnRcH8mNRnlYTKmfp9kogu6r2FbWRO5yeDmfNYN5NC/1eQvZsKnrA2YZ6JtB8+1+r6sVt5EeTbMZvERDsLrWlenBg9ZOxCH+3OZrIfevL3fakDiTj9DU+Dv5b4XId4Nh81NLXP7xCe089wjj6i3vrGhhHAxVbx50dbmFXZ75MutVYde83I+2bZLqe/7Pnz9ssdsBDYU4i23cx02uRneH+bhbb/m/S8T9rIKfln9b/s0ch2SunP945aTH65hWH9vn9dQaDcccWtrHubT7bVmYNl7sNenpFUGVmlg+xmmGmy7oViwrrUB0ZWgEP3NjnYGZ78Ax94LL35Eif2CHrvBs+hM50e9CM2bV5xFdBJ6wk1xQCytHtc61JH6kHm1xqLBjI1vTbnMbH46h9+NOFs0tJ/J19cQDmWPfXBzuR2uy0K6kOvKF9GFwKKRjBH5IhTulGDbHfrudINw+mItKJeaN2+etRFsovegRVASThpOjzFvltdiJE4mdZ+98IVAz/Wf3aJ/vR3HQvoWDaA3SGztZlhVB/XzK9h3SEkb0DzzjHrrH/0ofPrTGpI/d07JoFnOli3BvFxr9wo9uS7nnpdz3MuhbCM7aypjj9nrh2S3nFsfhqvtvS0r4ZdJfjgffrj/YRRhaKwsk/qy1z3Mzdt+l/Pi9nqLEAzz68upgKGnbq8Zvgf7PO04NiRnaDw1jUZdhl35lvP5y+LE5el8Ivp9zC52ub4EvGKiz01rdlIaKoIK9gVS0vaux38fjr0fTv0enHscOEPfXvZCGPU3q9f2uWbb/uI1zD5sxxpnOS/s9K+1qjVxncsDXCAbA1FJdX5W0wZGSubhutCHy/04h9DX+nayRuphhcXENhsCs+iWZ+FwM7vtLJ0rEXZdzpfnfvopf3ZiYfe44NDeEydfVXwfkTC1u+R0hBk/0IfSw8ATh8FaTSFkpL2HRw59uH4Xmef7sdM1L0R8sTdQiFAf4XLn0Zfz/OohJRXGPfOMlrV9+tNat/7009ojfmtrtzJ9L4j05GTT1ixnPezAtixeM5IaCtCMaOfz3dsOt4OezI2AhiS/HNpfjjQM92ee8fA9DD1tO9bwuMOhNUOiht1Gwl659WF0Yvj6ZUPAjjV8HHpCtzC87ceiFRa9GEZJlkndPsdhOsFSE7ZWS3EMP7uu6zsQ2rGr6lUQ44mIA74d+BvAH0NdwZGInATeiw6ZefzKllFwWWhmcPpxHQpz/CNw9mFon+fCYfghPBqOr7O3nke2LmJpov83kVnX9h5rtNZUpiy3GvAagu9D0d2Oeugzy11L5k3Lheepc36UJ8Md0BI5lz3+ekXXtSDwOqcG6OvKJQFNL2YDsEY0C2I073dQspYGxooZBzGfhQQWefRFPjxHAJwZFBZGH8QSGZD4Ivdun7eF6vOaLIcfc6gfE+INdQAWTchrN0K3fcaElgdaPr/LdweGwCWinOdXB12njWeefho+9zntMPfQQ0ryp09raN5yshfDMMw8nOY2JBd4KcEa0Vj3NmvXOgw1Q58GGBoEw8Y0Q4IfqvGHfettndYgZ9lrHXq8y7nwZS8aXhpKH75+Wdi3TP7L+fRlId5yusG2GRpX1sRn+L6H4XfoIx7LRtKyiG85FWH7G661bXXKn+kT7DtYWenfr4kTrxSX4tH/NvBB4B8DD6ekV0oROQL8aeBfici7UkrvuPLlvDq47z548UW9PwwZDa264Q9lr8f3avNoYZflH+hyh6cQ+jyaWYcmmrHnbaJTCBB8Yhy2CTvPUJ//JNXGZ/Abn6fiKEG2GPk5VWgIoaMKY7zUVL4hhIhzCUfM73GEcx5hjHgPwSNJsucpmcwzuQWvXq/PtepSATnMTAAvvQfJTib1qI3wkp1VowGJr2gzG7eSQ+urvWcepvS58xyuTgMvtcvd9WQTmpwLTwNyk4GXu/CSGZBiJmFrmWtfPK4ncmufu1iDkbrTx9Lgi94Fi5HaZ9HpyNtFtMCurnnkluX1F8NpYr9O2za1+b1Y/h4WuX/sj2kVhpEAu+/1+5KLJHRfipvuPL+WSEkv0idP6oCXL3xB8+mf/zw8+yycPaukboK5l7tYD73lIZkPvXArJxsSKuz2wof5Zbuu7TU+ddiQxm7Dx+zYsLvMze4P0wEWth6Gu4NPJJLu2yWQhHcgLhFCyoFBfd6yWt4lDX/nx/RaKHoK6jvV9yz6V5wgIngn+diC87L4PIZRgmVYlcBQcW/qd3sPtk3T9IbRkCfsOGZMDUl9aBCJ6D7sN2BiPcu92zHtd9K2ffc+i75cTJtxKbgUov9zKaWX2J8ppdPAO4F3isgNlQj81Keu9wouhhlCzP5fyvcj4jpE7kTkW3DyzXiJiES8izjX4aXDSUfwHcF1eN9SuUgIDcF11KFhVM0Z+ZZRNWM0mjOuGib1DpO6YTxqmdZzaj9nOpmzMmmppw1TN2c0aan9nElomEwbxqFjVLdMV2A0EqqRJ4xG+GoFP1rB12PcaBUJE1xtJW15gpuV5YkRmtWVi3rhkj3smOhz4lENjIU3nneTLGSeQ+ne9h/o+9PXYIJACYDLpG4kPsyDYzse/N/IdkeNjGH4PEaQLnfaG4T9YXBmZpkygyE2u4g9atpi8bjL78siAHk3zrPoHGjGB3a4DtIsD+1p8+c5g4N/+JX88G668/xqoWng/Hn1yp96SlXvX/iC1qq/+GJP6taFzby9C2HZizWyGOa2jZDn893h7WWV/NDLNq992Ct+6G0uk/uwLauGkDtSiqTYIaQc09JrUOwSdQUikdpHRBJO0sIW9l2Lq0SvS06QmPA+EfLriQ7nEpI8rolIEIIXKt/hRPDZ13AOcJnIEVLnCJAJPZFEtHDHiR7fOXyQbDCIrjdIzsQJscv3nccL+ErwXqhroaoF5xziHF3naDtH0+z+LoZO4NAAGooG7XEzBIYqeiuls/D7MBph5D+sOlh2Fq1Rztralf2GX5bo9zr5L2ebgiHm7M6ZD2JhCGoL9/8HD/ECpumu8aV75XoHoq0BHGpVi0T98UlSDhT1/oPrcC7hXcT7ROVjvlAkqipR1VoKP67VCh9PI+MqMR5HpuPEZNIwHnesTefUdcvauNXHRpGV6ZyVUctk0rG6EpnWHfW4ZTwSqioSgtMquyrg3BipAqJXgOx959D5wiPPkQYjcvPGF55/fv929Yxt71kvQulp0DEv9SHzNPhch6H1xcCcpEbJ8HOOXW+wJLtq2/rJVwRzyUzBY0ZHXl9sNJJhx4lz1TakmZJ4u6X6iG4HTV0MtAip0TWs/GFYvfsCv5ulX8mNep5vb8POc7D2BghXVoPUdUrYx4/Dk0/q7Utf0tuzz2o+fX29F8pZO9eLeVt2wbb7lpMd5teHXeMspL+cvx4+Nqwz3y1663AyVyKqwflIcB1BIt5HnHRIAi8NLiX9+XYd4iJxBk7iQt7iXKfGgOvwdJnME0LCoYTunCCxwyOL510+DUQcPkZcSnjAe1GidZFQCcFHBJfJ1Onl0EEQh+sgicPnqY8+gvcOEUcVAOeQpASvn6WHzpFESE6gc9TB6VBIB/U4RxNy2rDrhNgIs7noGZuSBjEdJCcEBKkcDoevPM4JPgijkaXmesfAvH3ovW+LxNr3ZVGB2az3zs1AG4168p9Mdv9m7Psf9ie4XFyyGE9EPgL8hZTSeRH5PjTB++MppZexX/cfVle1XGUIs4avDEbgaY+/RubyCv4OSXqvEK3dX35tWnpumfzJcYIEyas3vedxhobDbtNDSDgB7yPiUh8+8wkvCR+SmighEpyosRAiISTqOml6okqMRolRnRiNhNEoMp3AyiQymQrTqTCdwnSSmIwTqysdqwciK9PE2mpiOu6YThOTcUcVOuowI/hI8AnvWxwdIkbYFuYfkHdCCZQupweERU7fvG6LLLzEiDJz3+KnmcgJUOdUAZLD9NZ2d96LAhdEPlfCnm/392MWDZrB0eWyvthCYyLCnCKYbcL6UeA0cG7X98Szz8N3/sZLvvuL4YY7z9/1J4CHlh58PRx6O9xxHxx+Oxx5K6y8TjUfIgvB06lTSuBPPdUT+7Fj6qWfO6fbzGa912XkfjEMB60Mw+7QkzT0uVezPc1bdy7hXEeMjXquISE52pNiIkrCpYgngbQEIo4W5zs8EGROFUBSpKJDWo38SczRIYmkxhGdqLEvKpD1IWWPOi28Z++SEp9YCL5DnFdvPp/z2sLBaUjeQtcBvNd1hkqvBU7UGFiE3hGcU2NYnODyZ6dhfL0+OO/wzpGSRg4AUuNB1BFqW8E7NDJQO4KHqgaPQHCkJLRdTbfjid6h8YWY1+6I4gjBITg1aiqNFHif8L4j0eTPORt1m0JKQpdAkiOMPJOR4EYeFwRxga7ztJ1jPu+/UyN1y7tbWnZZqGgRgLbtjUmb5jefw5vffLknyStT3R/MJ//XAN8DvAf4D8B3Xf7hrw/qek7lO/XjBhFWC5NDypf0mOm20x8ISckxP58QjRAvHif7yfbcbqK0VzrIDUqH3ntPyPoqWwGDfSz/Neje9n7uQq/dg7gWjy8/tnu/Kb+bmKBtHbv32e/X8nAi2QgQtZytZ453aRGCU1lAyj/6pI3oSIQQNYIQoAqJqo7UVUdVRUYhUo8i47pjOumYjhsm45aVScN0nFiZwnScWJu2rK00rKw2rIw6VsaR8UrHpOqoR31I03nN8S2iBCI5HeBZlK7FSD+RrmPRjS526mmn7GV3NrnOpLjW5moYws81+F3HQlDY5RG125vQvIBWTFxubc3vXc6LbrDzfJnkAY7C2aM0J9/PznzE6Y2DPHPy9Tx7+h6ePnEPz556HcfO3suL51/Hue3bWJ+tsjMf08RA2wkpeZpOf8Vdp8HnlIcsDZXZQ5HaIpQeE13X4HynRA50UUlarxkJTwSJGnqWLoeZo+ayW73meBf1JwPUVURSh3NquNauwzvBpZaqUpFmVVv6R0PWGmmCNjm8A5ftVXFQVzP9nYN61iHikobLvSMb6REvgmTD3eXEuXj19CUl/CgxEnAhEiQSBjX0JJDK4xGSJLzP10qXcEFwRJX7SKtefGhJuOwwOHCR2PbRMIkJXKIKHaFKBAc+COIdghCj0KVEN/e0JJi5bIfP9FraadDPi8OLI+R8fhUcyXuNQHhPQui6QNM6oGKHoFGBWpiMor4PERDo2pauSbRzTVO0nRC8rqtygjjPeOSpR6oNciHgQ+aH1Kd5trb6vLzBOTUGjhzRa9PBg1d2lrwSom9EJAB/C/hXKaVfFJH7r+zw1weT5lF20l2kqMkRISFOf0gp6U1QvZkA4pP+0PIvOElC7caEiD5uFOehj/QKkIQuxkz7SvOdypwwOheEJJJDXmosJFwut+5NjxiFmIQUZWGK6PksQLeIG+R3xMJD3eXZL3vpFyL+l8Ne2+6OHkTInvRer3npsR3mSQjiY/YCXM7J6WcdPIgIlQgpJGqv79QFvXBUeZtQJzUMvHoVoxpqHxmNOkajjkndMpm0TOo500nL6mTGZDRndTrj4GSTtek60/GMlXqL1fE243qbOsyoXUNd7yw0EbLohJfJu41Akwk/oT37Gw27b29Cewo4y6VVRlwJPLzmf3c5L7yhzvOuewNbsxN0MXB64zBPnXg9R8++nudOvZZjp1/P0bOv5fT5I5zeuo2NnVW25yOaNtDEQOyErsseGnMSc7oc6RKceobouedp8SRi1LN4hEYG2s7OYkeHW1wHuthHyBwdiUQFdPls9Snl80NJGInEqL9XcYJ3LYEOfEMtCak6AhGRjhASEkWzVxEkCE3rEecJ+TwRrw6I95EgGoELIeK8Gd4tXmTRm0lcIkj20EXwwefHofIR5yN1SLgqUTmN5CU0HC8enNh5GvP+Becjzqlb432L95JD17pG1cM6UhREgkYIEF2Lc1SrevWr6pQjH2qAtI1eXLtOSG3M3a4TIWiqTHtICUGEUIm2qcjutdDgg15oYxQNkCWB5DVd4BKjCYy84J3DhRwzaT1N44nBa4qAwGgUkLHHiSMEYTRKBK/X+eBbhIbYzXQKdYKdRmg7Yd54YlLRr3iPD4HJ1C8mBVrTI1BDoG1fPpL0cnglRP//Bh5EQ3k/kB+7wg681wc7zYh59AgeGxDiAReThlKy+ZvQsBciGkKTTn/AkhA3h5iyaKRVwicRnORwsYbGUnZhnYcgEZLDOT1xuuQ1T+4hRhmkDvwispzQ/G2H5C9bw0ciEJNbhJcjQtdpGCxF/eFGJ8QEXSdINhK6lMk4aj4rJkidviaqQ0FnQu+XhP7NUFgO818o0nAxDLfVuFxEf9BNBFrTJAyPx8KEUe8japjP6wXGk/KFS70lzUu6nLtMVB5EnKp+pdILjwSCz9UKLlJXkSo0VCFS+4ZR2GFcz5mMdphUO6yMt5nW26z4dVbr86yGUxxaOcF09CKr4w1WRtuMqx3G1Q51aKh8k9cRdwvkLxsePQUD2ixopI95kwLbvPoA9/ypyznANT/PReSbgX+Dvpn/mFL6l5e7r1/43W/ln/3Kd9GmijYG2q6iiYGuC9nL88ROICbarI0QScTOZQM60REIQJt/64HcECnH5WocHTC3scl4OovyYLI1z/C3auaC5NSd06tB3l5J3jkI0uFTB6Gldgl8x8hFOjTl5VJEKjWCkwRIgaaLVF40pC0gohEu7zqCgPfdIp2WUiSECOJznlpTUt4L3mmevAqdkrKop1yFduE1a2QtIl69e5AchdNsvQ95PyL44HCI5sZ90u1T1PC7ZF2QkMMfLNT5ftRoON2U+T5fjyQgOGJMxJQ9fam1PxeWV8/h+6rTU0BUSJhcpHL6WZMi3dyRxJNSYN4EbXJTR+qRhmJ8aHUkR6tkHGNLco5uS/CVU12B0++hrh11reF6RFMGOE8XA93M01Kz3Xnabsy8cfk714jmqOo4eKAlhB2Cj4xy1ZUZAO3Ms7lVcS56uljhvF/k8q8El1JHL0nxkyLyTqBLKW2LyFcAHxtuc2VLuegartqFAdTR0kB8h0pLHDGLrIRE1zm1VJOQvFqkbRTEVXqqOxVlaQgLzeM4/eFZ/tc5oZNI5TTn27Uph3xUOZraoKa80zBVkBwuCwnv52ptJ6BSi9wHtb7FjAsR8IJPgq8iMalVnaIjOa+5pC6pk9m5PFPG0aVEjE77xki+aHV64qSoP/Ku0UtThyjpd0IbhRShaT0pqsHQdWo8EPV+G4W2g25xQTRmsxTAcnSBwd8Lfvu7tlmkDaLQRt3vrBkaA5YgSSosTOSLGHjXZA9EqxWC68OnQiL4Rj0mcbqtd3g8PkzwsqrCJt/hXUdVtVTSUYWWyjfU1Yy62mYcGibVNivjbSajTY0IjLZYHW+wNjnP6mSDtfEm03qTab3NpFZDIjhPFTzeOSRYsbAJDLPb5fJ0QGfFyXarWYzGlVwm6AIceN0lnxOv1nkuIh74MeC/Ao4CnxSRd6eUHr2c/f387/0JvnDirexOXw3dn7T7/2lopHY5XhazFkyJTKk5l1+qFI0+AjX8a2TvB8ewKAB5j6KhejQC5FIi1AmfOrxPIB0+6W8yuHz8FBDp9JrkPK6Fzjn1ip05FxEf9PcdgpCchd9FnQuBJCqUcwI+dFlTo5597fVd1qGl8hoRc8Hhs8xcRPclTo0jjahle9JrFCs4NawlE74GIJOeY1EW+3I46gCEnAIgqXZWlPhVFa/XojZ20OaSOq/XZ1CjpfKRqmpybypR58oFJEnWsQoxD8nqOkcbNX8ffMdo1Oqzfg7sEJNT7UUbcS4yn1c4H6gqT+0FFwKhyt25Q8xCu4RzLV0rdI0wnznaztNFx6z1+XcQEDcjVOrhr60IofJUI8doHEgEZk0gphFN69jahKaNuNgRQouXjul4zmQSmUxUoDddCYxXRsDlS+8vqY4+n/i/llJ6ZvD4M8A7ROQn0Rrc/3zZq7gIrvaFAWBnvkLEvhi1s9WvDywC4SkiJFwnuC5lchfERSSfUPrLztl5yYRPp6lXAZc6upTyyaHhZxOvuCxvFWERMvM4cBBTzgtGIe2oGEXd2JhP3ITzUU8op5YsyeF8wkmDDzMqlxj7hlBHvO+oXIIQCSpGUA+TiMeRpKX2KV8nE5IcSRxdEuZtoG0cbXKaj0+OplFCb6OWpLStRhDazmk4LCZS45gloWn0c541jq51+prG03aeJuoJOe8ke0gaAmWhYiDflz1u7PG3RyJ7cEgOoYN2/ouLLXIMgUDC06oXJO0iWqDKY1UuaylPiyfifIMTofatGgZevSn1qNpsWES9MOWcZvCRumqoQseo7hhVDeOqYTpuGNcNq5MdViczVqczDqzM8/2WldWW6bhjMoZxDVVdU1UePxohIc+197lZkV9FGx+t6GMrb3olp8WrdZ5/LfB4SukJABH5eeDbgMs6n9c3x/S/F/sdXKhCZYgE1LvMw/6eGQ1Dg2EvMa2RvW2f0P4GklehwfxAJIp6rDjBp6SPxo4YHa5OxKSiO0lJxXPk60tSAZ7P3RqjOIgtISRSp5GsLiZqOnUSRMPrwUccmq6qa/WuK8lh7ayZ0euHOhwJIbUdBNE1WNlb/lgrlzU2QdMDznsV0fmUBWxacifouSMuLdT4iKZGXRYEOoQYPc6bU+A1HRei9twSoaojMUUcApaq8KpvkqTRzy55kBbnfb5G0wt/R2jEsnMa1Umq2p91Y90uCHXQHhzBRUajluDmRDNgJNK1kW4emM8qoqvZ3Ay03ZguVagz0eGcMKo7jqzO8SFShZSV9J6dWY4gzB072yPOdqr1UGfOU48cayuB6YpjPHVMViqmK2NCpWmGlDrmOw3bWy3zNnLwjks5I/bGpRD9NwN/B/g5EXkjmmAc51/4B4B/nVL6zOUv4WVxVS8MADtpDX0LeyPT9eB/9HHlhcfYahkGrYaOZY73Ee88wUVCzJm+UaO1rwIkVYJK1HCuz56lSGLk5+ASIXQazqLFBaFyHbVvNUzn9MKRkhCztdx1VS7PCXQ5pJ+iI3YwmwvbUelcTxnBpQROPVyXa2Ej+SKUL0beqw9TVw2V36H2iZWqJYzn1KFj5Bpc1eG7OVWlxFi5SIPDpcg8VuzMK7rGszMPNNFrSLWtaFqnIpTW00ZP0wpNOyLGyKyr6eYwbwOzbBTMZzVN8sybmjYGdmaBOZ6OgPZxt4vt0FCQwX3YbQi4pf8nbFTNokyusy/c/iYcLR5y3W9cRF+CdCpY8p3mR9E8q3MJcXrR8Pk71dCoCne8yyIm7/BVJDinc4KCaI5uDFXlcjWCsLIamEyE1TVhuhJYO1Bx4HDNyoGKtbWa1QOBSe0ZTxzjsaMeOeqR7GECXRCv1nn+OuDZwf+PAn/8cne25e7M915pXuRC2+8ViVq+P8TwdzIUtGpmPsss8QlmSc/EptPoncue8vYsEhxK6F4979a11CmRnHr8GmGC4LXsNbgWnyJSRWqJ+DrhYocPOb3o1LgkCl3U875xiSop6Xov2l4CVEEeHFWdw/A+RzQRNW7zNSp46LpGS+uywyFJIHocSqR4jWFISnTO4SRfc5KQcrMc7zRnH3w2tlMW63klZu8htQ6RoJ9uowq/4FTY55zGY0dBI3HilMwlryl1MEsun2tCcKp7qKrIqN7JpbqSVf7CvPV0qWa7cSAVG9uJpsk1j6IGmHctddhhtW6pRx3BC3Vd4UKg6Sq6qKmjzZ3E+lYkRsFJJHgVTB4cbzGdJMZjmKw4JmPHaBqQXGY7nws7244TpwObW4H17ZrNzYqmC7TdhAOHAn/8WhJ9SmkH+HHgx3PDjNuB7ZTS2cs/7CvCVb0w9LAwMux90u/1XH+yJ+rFhPa5lcS/pPuVeY1aplH7hsq1+Kqlloa60m52XjqqfMH3ABIZhY66ahmFxI6rCNJqTmek5TS1UzIJdUtdt4zcDC/twoCofA6LieblpEOVrNExbyuaudBGz05X59x/0LxlSjRdTZegmwltEraBtgtEwsKaVuFpbtTj1KPVXHiDdx21n1O5LUKYs1bNmEy2qEND8DtMwpxR3ah8Ka9pZz5mpxkzjzU7zZjt2Ygm1sznI5oUaNvArKnZ6UZ0bU2THLN5zbzx2TAYsTMf0XReFdTNiFkT2Ip1NgrMGHBLtwulEXZ7her7J+z8hwSteX8pawc0XRC8hiYrl0guLdLnoUpK7PnQ3glVperc4HMzD6e1u+KhqlQVHIJ6PaGSXc00rF7XuiqOxznUN9UGG9/8zfCmS3Tq98F5voCIfC/wvQD33HPPRbc9Hb/m1VjSReCW/u4dTehy+F7JX39NkiKug9pFEklD4iJEmeOT5tcdCQnZ2UhaBy9o1E8k4rpIDC20kehyp8uo20Yki/GyXiWH/b10+jvNnneV+0vpqAengYQsgiV68JWqDRKEWjVGiTZHN83YzQaAqCOiJKvF4FomqL/7mPT/AsTO4aqgDSCTIJ1FFaPm9NM2Va7OwTlEKpCYI46ergtqkIRESKozqLz2+dCop+C8qiPa6EnJMZslUvQkgaatabNhodeziA8z6iqxOk2EyhFqqH0iyYimrYltousS2zNhY6sldi3ebxP8FpXvOLTimUw9kymMx4HxtGIyFkQ6UozMm8T2pnDmVGLzWc/mlmdj2zNvK7o20OWUzniqfUVuW4usrsLB26bAXZf9K30lYjxrmPH8ZR/tGuKVXBx+5nu+j2dPr7LVrrC9M2I2n3Jue8rmbMpWs8b5rTU2t8dszQ+ysT1mu5my3YyZMSIuPMkhcVzMO9DtOmC7m7BtJv4CZgxobXRNq+Iw3xJcVKGM66j8nLpq1Vjwsyz4ahlVnVr7bgXvI7Wfay5POiaVblePtplUM+o0ow5zxpMdqtAoARFpktYIdcnRRY0QRPSikbJ4CISmdUQcMToVrLSBJgXmbZ0FUJWWJiXPvAtsNSPitobNUvQ5FxezQYCGxlNHqDqqMGMcdqj9nLqacWT1DKN6xkq9zThsUnlNQXivOoGdZsLWbMz2bMy8G7HZTJg3I2bNhDbWzJqa7fkKTRuYdyOarmJn5mjiiJ1ZzVYzYXNWE7uKjZ0J2/PAjNzmd/Hd2nc4jBQMv9vd32JCgwLNIkSwjFy3m+t3Q5CXDOUY9uMe9jq3tsv2dzhNbHnYiG331rdeOtHvei/X9jw/Brxh8P/X58eGx/8J4CcA7rvvvotqAh5/Yq/5nS1LJ9kFYBG63OuAFu2F0VLTMBLt3JZo6FphjqfKsbwZVb4WCJoSst/JXtcEe84ut2nxb0di2yYcNppaG7k6/9Y7mqgENgodlTSkrsMnPb8JqvchQkBz4l2MfR7fcuC5/n6hHAhCTI4uOlzsaFPMUUkNR/vUIUkI+VcdcrDCJ40Q+eggCLVzJBfw1Uj3nBz4RuOHov0iPKiYbi6atvCipJ21UdKJRi69Kesj4oI2vmkD4h24juAdSdSzrrw6CMGz2F+M+rl3qPEvLtFte9UWSUIiuKCKLKSjqh3T8TbjWtMfdYiIczTRkVJFGz2zHZjNhPOt4EKXSw8doxqmhyOTccVoFJiMNP02GnmEjq7ZZGcrstM4Tj7n2NzybO6ssLVT06aKLo6I0RGqjlHVMR51HFqbcWBtk9WVjvEIFVcGj/ig2pzqUtJRF8YrInoAEflO4FtZTP3gv6SUfu6KVnFxvOyFAV7ZxeE7v+k30OYiF8LwIr8s7MlimyTM5p6zGys8f+pOjp69m8deeCNPvPhGvvT8G/nSiddydv0uzjSH6JjQGwfLRkFvDIBeZuYdOXxsOT+NCoSsLKirTstTpCNUGiWoww51aKn9jFHVMPJz6mpHRWK+1YZyoqG4yjdUYc7Iz1kdrbMy2WI62mFabTGpNllZ2dBog4YBaFIgiFYWRDzzJjBvR7RdABIxBbro6VIgppT1ByCkHAnXgr+mhXkzYt6NmDU1XayZx0AXK2bzmvX5QeaxIiYVuLhcVKD6A/VMtLytZVzPGI23mYSW6eoOR0YzVkbnmYzzRct5tcKp2G7H7DSrbM6mzJopO82EWTth1o6YdxO2201mszE7bcV8XmnqoanY3vJsz9TqbhvP+Q3H1pYwb2HvyMDLwxqmXGyoyXKb0iH57zXec/jYkPzX1y9pSZcEEfn+lNK/ugq7+iTw5pweOIYO0vnOy93ZZKLN8XYjCxiBw4fhDW+At72t4w+/ZYM/8uVP8RW3P8bt4bPUO1+kap7EtWegXR+MKs4NiWjphXbD73g5Tw+gFTuzmbDTBs5uHOKZE6/hyZOv54njX8YzZ+7h+KnXcHrrNs5uH2RntspmUzNrRsQY6JInRU9MQhOFJgV86xGnxL2TNT6VRA17u44QmuwQhFzH3mlZWuiIbYuvhTah0UA0DOdSR2zViEidI/lEwhFTh0QN67etULmI6YXbDnyMRA8yV6IMCTonIDMV3vmI84JPQclJPBLWcL7T8zG2OJ+IMeJkri1ypdVe9gRc0lJa7wUnrar9J+jnrx6CigwRmq6GKGw3mvNOMVfZuIjITJN5QaNlK2OhrhPJaaRCa+u1QqnrhPkORCo2k9P1ewihpa4aDq5ol8961DEaCeOxYzyOVHWgmWv6cWcmbKw7Xtwes7UT2J55ZnNH7Dxdq4LHKiRGQQW500nHyqRhdaVlMh0R6oD3AalzBU3M1/yUDdAu99Z4xampl54RrxTfmFL6dvuPiPwYcC2J/qpeGBQXI3m4+EjXTGIC41HHa0ZzXnPbGf4IXwA+vOcrYhQ2tmqeOXk3nz36Fj7zxbfx4LG386UTb+TFM3ex0ZlmYNlqE/p54qOFzzFrzPNIhJnKWZx0OtkphwBDanTQTdUQfMuk2qEKM0ahYZR/yM5FJLXgoMpK8tqrIRD8nHE1Z1pvcmCyzsp4k5Vqk5XxNiujLQ6Nz1LXM4JLWuaHRgG66DXMHz1NV+dOUnq/yWmCGFsSsyzU0fpVqyTwLpLwiKvYmE81PJ/GzJsp827CLB5kNh9xLo1p5xVpXtFt1updSQBf5Q5ZgdFYmEwdkylMD3hWVwIHV4WV1YqVaU2oPMl72lajFPO5sL0jbG0pedhtPtfb9rY2t7CuVbOZ3t/a0k6L9ndnR1upXm7tqw22uBCWPfehQTD07E+cuLzjA4jILw7/C3w1cMVEn1JqReQfAL+B/uD/U0rpkcvd30c+Av/6X8PXfz183dfBl3+5Dgp5actQDxwE3p5v/502OZqtw+bjcOZROPcInHsMtp+B+RnoNnLbYbO8B5MCXyL883pNGDvGdBxaPcW9rznJN/AwvUDPXqNK/ZQcs7nn/NZBTq0f5ulTr+e5s6/hudOv4dT6EU5t3Mm5rQOs76ywE9U4bRvPvKuJ0RNFVeZNqmgFfJsQaQhdh6chtFpJUkkgBK3t9pWKRNuuQ1xHHRNt16lgL0Wty69QcWCnIXhJMVeqqBGvEfmoTXuy8SAxK/Q7wYuDpL0CXOdxlcM5jX7UtUfcSvbe7XONxNRCq0aI9hDR8HzwUWvgJYK43JWvpa41HSFobl+V/5CSI0iicwm6RNMmHRAjkqsKkpYBBs80E/l4skNVJcZVu2jAJc4znztmTWCnrVg/53jxuLAzq9mZeeaNXjNiCiRxOYWWGI/mrB2MrKxEVldgOoGqToTK4/0Ki+FWxNzCelPJfTtlaUedWznn8tmQw3r+yurrLofoRyLy36B589cDkytawcvgal8YrgecSxxYnfFVq0/xVfc+xXf8yfctnosRNncmPH38tTz07Fv45BN/lAef/Gq+dPyNnFy/k61o0YChR9F7LMoH2nt9Z94QaBk5mDuH62r8XIU06yFqDj9o7+oqNIwr9fonYZvKt1ShzY2oHE4iPkWcVzFgyCd6qFumdYP3ahSsTmccnG6yOt1hOpqzMu2YTCLTSWQy6qi0dofIhDaN6BjTpCktYzpGJFboZEyXaqIbMW9HNGlMouaABMRVdL6GGHAhgA+EEAiVA3E0nWc+07TCbC4LIt7ZyV2nZurZNqd3N56wvuPWjnJlRVsjr6xofvvOO/Xx0UiJ08i363pyN+K3eeJbW3rMnR0l/Nmsb6G6uamDUex158/3g1BeKYZTtS6EEODRy5arAnA+pbTouCMi/+sV7W2AlNKvA79+NfZ1333wjndc5oudh8khmNwHt9+nj8UOds7D5mNw6gEl//Ofh+3nlfzbzdw2eRjqN/SVPH30Tkuu9P7uL1skMR51jEenuPPwWd5yz1NL+1KkVNG0NVuzCWe2D3Nq4winN49wbrbG6fUjrG+vcW7nAOs7U7bmB5jPanao6LqQK1yEFFXFTdIqlJgLi3UGYmA+97SSqENDyjlyX0Wa1OISWqbrk9amd2itu9P+It4lJEZc6/Eu0c21T0gkQozElLQvfROJ4nKTGMFLRecDzlf4MM5TrDutXkoNoWpxXcJLo3oE77UBj4Qc/Qi5P0luyUvUfL2DegTjkdapj0baXbCumtzkKoKHtvFszyqaxnNuY8TxtmY+q5h1gbbV0uHY5f6mLlFXmv+fjuYcPiRMRy3TSWI67fI424j3uj5tARqySCpHfbr8vVpZbFiF6hCLjptG/u223m/O5Z9SBaMrUOIB8krLYkVkCvy3KMkfBX4lpbR1Rau4yrjvvvvS/fdfpJnXz64Cl7PkvcLuL7f9xV6zHArsVeJd5zi9foDHnr+XB5/+Sj791Nv57DN/kKdPvYFTG4dprWnKnug9kBGddrSqu0V5TyV6cjqfu9C5RF231AFtFBMi1ThprigkIGhNbfDEqDWzoXKMR4m60hPXBa/K3ZFQV47JWJisONbWVJiyuhY4cECV4JOJsLLaC8ts/KYN+DASG963iVzDqU+Lqa5pN4Evj6i055umJ+mdnd0euxHybJbb0ufTwnpUTyZqCKytqdjt4EG9bwK4EHpjYHt7d3vLrS0ldTNAZrPeSNje7g2C7W3tsb693RsGGxuXP4/6q78aPvMyOnkR+VRK6b49Hr83pfTU4P9H8iS7VxUvey6/GogdbJ2As4/A2QfhzAMaBdg6Du25fGEe5vmHMJJ3g79mCOSL+0tKSVn6awaD/V9D4/oSBylohFsqbdLSVmw1UzabNTbnq2w1B1nfWWFjtsLOrGJzp2Z72zNvPDtzoWtr5inRtYEYQy44FZJ4RDxCi88lcrIYkKNesjbGUdFb5VscEKqI+ETtdLqcBBbNbLx3WrrqXa7vJ1eoCN57fFUhPuB8UFGqE4K0/XTOsK2piFwNQB4/rWWClSr/8TSiAt5mLtp7vnE0XaWRkORISTvcWTm16aKqWmdvjCeJcZ2YTGEygtHY412r6911Wc+109YByB5bPJ/viAeXp2Zq96BBJti+U3QfrlLy7/JsjjjT0tnbLy48vdC5bL/CS4KI/Bngb6BlNw8Dv4nOrb7cRtzXD3/9HP0s9YzFFDPY1XxlOP1s+NiF4rKLgSnL+8hfuPN7vYh+IpL+9eK4Q4Q7xPH1oj+irhNOnRYef1x46LPCpx6ABx6A55+DEyfdYDxmb0zMEGb5+mPjEt001/nna0SMepmaJwh2a2DkNJZQVWgL2TyS0SZw7QDnt3bniMedEt8swtkteP5E/xoRfW5lZbdK/OBBJdGhYtzGQ9rHvGwMxNiTs9322taMAxvvaWS9PM97aHDMZkq0ZggMw/OnTu02BiwyYGMo19b6Y6ytwe236//NqLGIgPW2Hhocw2Ma+VsqYGgg2MCVzU04c0Yf28sYuP32vX+iF8PwPBeRh9Fm8g9fD5LfN3AeVl+jt9f/WX2sa2D9KTj7MJz6FJx7ADaehfmJ7PXP6Ml/CCPtll74adeHl9bi9/X8Kd/XHn462EjyiGT1ECU1VDKjGgkr9Tnu4Lh6gzZLVmolGj8iuUAXa9ouZM1NZN4Isx2Yb+s4l9k80KaKWTNl3oyZxRFt52njiJgSXfTa0CbpydNJjmJkA8GMFMlGgfcx19EnHJUSPEBKSHREIinN8dIRnSfuOMRXNBKIMgapSO4A4EidnewazdSpk5m4pR9MEyqHr2FSdxwYzam8ZI1Pq53xatG6d+9VH+DRzzqh319S50hDHEEvnL7Oso2Qt80zKxYTK/PFdUj+ibzG/B13ot9NboVLarQGO4oOuxIjfwd+BaoDV/ILfkWh+/8E/B/Ra//bgL8EfCXwFVe0gusBP1RV3zjwFdz5Wr39b75BH5vPderW5z8PDz0En/gEPP64TuA6f74fgQlKLBZiHpZlWXtF86C7rs8/m4c83HY61f9b5yYbt2le88ZGT55Ggisr+rqmgdOnWQwFsRGetr/xWB9bWYEDB/Q2ner/V5YE1kMv3o4/jAoYoRqpmu1ldpoZDPbeQc/P6VRv9v/hXOrhMIrNTf0s19f1/2YIPP98P3UKekPHPrtDh9S4WVnR+7ffru+7qvrP0IjevgszBCxCYAaC6QHs+7J1nTsHf+/vXdbP7OY5z68lfAWH3qy3e/+y/jBm63D+C3Dqfjj1STj3Odh5XkOwcYfdIj/oKwPsMmwpumEKgLx9X6rbRwSM+JPmeZNNORSQRrfptnKouModcoKq2V1FcBUhVIyDBzfR/QWXLeN5Pinm0G0rkTkhxY6YamIcEV1N0wa6OKZNni4Jbacec9c6OkL2oH0W/I1IzgZkQ4w5EpF73S9ONNQwAAGnjXUkdZpbd4KvHc7V+GqEDxoFqEIk+Ny8ihaRbRxNFgZHfd/mUVPr9wdK3kn0/ZKgs88VzYsLaih1bTaqEjSz/Fj+HcTs5aQckZGYDZB80SApoTtZaA3Up5zn7zMbAxH9nlzel3T6vYpkI+HyccmhexH5nZTSN17R0V4l7Itw33VC18Ezz8AXvgAPPwz33w+PPQZHj8LZsxfO65p3PZn0M5LNGB2S3bDky3Lc5smurPQ5b+eUiMy4MA/b9mGkPp329eDDOd3DWdz2vEUDjCRXV/Vma7KxkMPQu72HIaHP5/04yNmsXx/0XnrX9QbEXgEce8zEcGYIDGeMm9e9ualGgP21z8XSD0O9gH2Wlho4cKCPeFS5M27b9uJAG3phHr8db3sb/vpfh694GXpeDvftt/P8hj6XYwcbz8PpT8OJ34Mzn4bNp2F+Ugl4z1A/9CRuxG+PmeffDh63v2YsZIK0k8GG67iwO7Tsfc4lexWA+Uo9fpeNB5+7LrrsZSIgrXqbca4TGlMmvpRYtGcOefaCC9gcEV1S1PcjZsikHLevdIMU8/0cwZCc8nDZ6BGXPWafveDB+0qix3VjCOMBqdsJjBoqabtfU551r6SfhbyuzmvN04Ks2EJl/Jm482ci9A3UUpu9+IE+w4XB2kWP731P3JDfo6ZG9WuU/BUPDAZyJGZ0GI68/YI/Nbh46P5liV5Efgr4NHA38GJK6Ucv+oJ9gBv64nCVMST+z34WPvlJ9fife07DvkNP1xBCT8Krqz3RGukNiX+oAK/rnsSHRLyy0l93huFwIzszGsxrr5fSBEa60BOq1ZlbyPzQod7YWFnpRXTQk/FwBvjygBkjdyN+86zn891zyIdRATNGhnPFoX+tpQuWPy/L589mfUrg/HmNDGxsZPFgs/u7Gb7X1VUlf7sdONCnPobH/0N/SD+Ti8EuDvv1PL/pzuXZhir8T/yukv/652B2XMv7Lkj8OYy7q15/mOTNaQDJIWZg4elb3j/k7Vv6ELOQvf0ALkKsMvl6JZcQII3UCPAeZNSnAVJuONbOQeZaAtY14LtceJ23F6/K8ZRPAus4kdC17VqHEXomRyNMUn59JtOI7jPm92E5ckuR2hwIN9JIRRixmBuRkr5/i4C0W/n9zFgIJ12+LT4DW+cgDeskGx1uyViBxThqcXocn78byfk7e5+xze/HLnDmXUn/GUh+X6Pb4PY/dtGf1pUS/Z+hr0l5O3AEnW71IPBQSumXLrqD64Cb7uJwFTGbwZe+BI88Ag8+qOH+J57oQ/19nl9hJGwEs7q6u6zLCHCY77ZZykb65qkOBW2TiW7Xdb0XaiFp2K2GH6YIhg1mzBuG3ggx48AI/+BBraW20LjVmg89cOi9a3sPw7/O7SZ9i05YasA+A0sdDEndvHt7zLzxYVjfPjP73Mwoss9jY0OjMefO9Wp9W4sZQfbezMA6eBC+9Vvh3nsv/nsYEP2+PM9v+nO5azXX/8LvwfHfgvMPw/ZRDfdflPgroKYX8NlfE/gZ8ZPJwufNXG+liuTdJwiZqDBPX3oSdfWAOEdQ1ZngRrn8ywyIHGJO5vXPWdSCm5dNpc1fuhpCJjmXjy3o+0h+EFJ0meyrvP7sWbuBrkHyzYgyuRyhyJ60iEYnLHrhVvV9+UrXFC3y0PURi0QO51vEY+D122e9iFpkD9+iFQtBHb1RgXlJZMMhp1EkpxAkfz+SjaA80Ej3LVDfBnd+3UV/SldE9HvsLABvQS8Gb0sp/aNXtINXATf9xeEq4swZze9/9rPw6U+r5//MM5pr3tp6KQGORr3HfuCAEqgRjRGbecfQGwRGtMPwvkUNLEQ9Gumx5nMltmEJmnO7t7fSNxMGmudswjt4aY7cdAKrqxoBmE53r33o6ZvhsqzoH/41GHkPKwSGRGz7sM/GKgIs52/XXQvDmydvBoC9xvL89jk3Ta/OP326/8w2NnRf3/d98La3Xfz7v4jqfl+c57fcuZySqvmP/z48/344fT/sPAPzc2g+d68eHw4l/ZBvFvo18o7qTZonLU4JxpnHn0klJc1DO1lE0JXQXA4OZLLzQT1lCUqgfqT78Wal2jHy+2kbFSfGRlMWzk5SBzLuCXfh6fZ95jV87vs1iJ08WciYyNZ6fq8+qKHA8HU5GiDZSKDNBJ8NAj+GMM2GTf1Sgu42BxeWrv8czPiRQe4wtxondxtVEZKRek6vpLZ/n3Ysi0TEkC9m9p60aRmj2+CuP3nRn85VJfobAbfcxeEqoWng2WeV9B94QHP8Tzyh+X2rC7ffu0hP2EMvva77UP6wvM2IP8ZeBzBU3g/7th84oES8sqLktrOj4Wwjs1mu8zDRnAn2nOuPP0wxmJdteXjL6ZvRYvsxvcAwbbBM7kOSH0YUlsnfTitLBwyFjhaWN72EPW5GkRkew/3Y9mYMmBEAvViyqnrDC+DNb36pgHEZF7s47AeUcxnYOQsv3g8vvh9O/j5sPA7tGZT496r+8WiYv87/zzlnyWRuIX+r9TbP2Luch+5YhP4tRC/kUHkOl1s6wVs+egwyQhvnT1iE7C3XboZHF9Xrp1Hvud3W48UsUvMVkBW5MROeS5n8h3n5Qch/4dV7dqcAsqFg9X322o5sWAxSGB25BjCH7Oupfn4ue/HRSt0EmKlGYfj5WJohVJruCPmxZCF/sicR1TBI0hs3VlWRste/uJZkA8EFGN0FrylEvwvl4nB1cOaMNl158EG9PfZY7+1baZt5uzZkZVhrbh635dPNix0q46H39i2fb8p78+LNAz90SP/ftkr6p07pGre2chpr1Ofp19Z6Y8OEfkaeQw/dNAIh6JrtfZiRYUaL1crbbUjs5pkPsZcOwFIVQyPAwvjDMkGLDgwrA4aCvSpH+2w/piuwtIIZDffdB7fddvHvuBD9DYjZOpx8EJ5/D7z4/4ONL0F3FuuW+VIElPRH/f9d9oZTm8lE+pCy5bzNYoZM7rEXky2IPz+XLF+evXNfqbde1cAkk36OJOR2vAuyTp1WJbQ5bM5cj2UePNnrN6/Y8uAmBjRDwtZtRovLx7SoAB6k7T17scer3mhIiYVIzmVjRlzO86/miELot02oodLliEVKQNt/FqZVcKO8VvusOxYl1YKuzeccPk6fT7AI+U/uhNf++Yv+LArRF1wxtra0jO+BB7QJy+c/r97/iy/2oeKht295dROKWZ4eerI0j9tC3E3Te9TjcZ9nt5D1kMwPH4Y77tD/N416+i++qORvqvbRqA/RW3MbI34zMizNMAytm/DNjAz7v5UCQv+YhdKHXrjtF3anEqA3dobbQE/qhmEnPvtrRG7/N6PBDCkzAszIeNOb+s/8QihEfxNgvg0nPg3HfhWOfwQ2vwTdOru79g1R07fczicigtXDqzfqskdN9rKN3EVz6wm0lI9MWCZAy6S7KFGrldx9rZ5xGNOH682gyNGFRdg7n5RpS73/Zoe+1Mypx+1NGDjKoe/sWafs+YsRu+XTfe/9m9jN++xFZ+87WEQjh82deQghHzt7485SH9P8vnIIP+WQveSohVUmLNaUc/K2va9ZVBuY0WJew0Ik6fQ7Gt8Bd//pi/4MCtEXXFW0LRw71of4P/tZeOopVfKboM/C5Bbit5y+Ea4RkxGrkdWQxGLsiX9YS295eefUmDh0SIn/zjt1250dJf4XXuiJv+v0uYMHdxO/EfawBt9SFKCPWXrB0hPjse5r6D1D7/1bGsL2bVicw9KLBw3DTn62rR1/qJOwfP+yETDs6me3t71NP5eLoRD9TYjZFrz4cXj2V+HkR2DzGWCdC4xURLuYZ+JflOG5XI+fvfahd2uk2OUfqTdiHzSmgD4XnWARuvejHErPue1qrMeuLDdux0D3KRbSNvLcVnFf2slh9JSNhnEmc0sXWIoin9iWqvBZJIelBbIIzkLpplkQO35+nb13l09iI+eFqM7EfWsaTZBR3hYWofl2RyMWJhLM7XzV4BmxKO8j6Gdq6ybC5G54/bdc9GsvRF9wzRCjDk8xFf+DD2pe/9gxDaubMt1gIfLDh5V0h7nl5QEtlp83L9aI06IFq6u6r6HIbXUVjhzRJjS33abbb27CyZPayOb8+d3KfhPoTae9ZmA87gnVutJZSN25/jVHjuh7mEz6NICJ6aD3rIekPxwru1w5YMccnpLDcbW2T/vcjeQNpoWw2+tfr+/lYihEfwtgtgHP/RY882tw6qOwcwzI/dRfghwqZ9KTkHnFbVRv38L1Uun24qGSrLwfEOVCcBe1uiB1fZjaQv1Wv291+2EKBDUAkkUFTGhjwpVc4y5zmM9U6Cc7gxr1vK5qrFGJKuf0rdNd7Pr3sCjhczkIYSE3U89bGM/p/kMW95nSf1HvnyMZ5qGbAeCmEPIFwuUGPDGH7WOjKYvU9eV+3sL9OQIile578lp4/Tdf9GsuRF/wqiAlLQF77DEN7z/wgKr4X3hBjQFr8GIwgl9bU1KeTlk0yDGCNHGd1dPv7PTkZsp7I17L7Q/TB4cO9cR/8KA+fu6ckv6ZM31XOxPymcc+9OKNnO34NqluNutL2g4e1FSCaQlS6jvVLSvph+RvKQyLagzV/0MjYOjVw27dA/TbDb3822/fHVHYC4Xob0Gsn4Tnfh2efRecuR+ak2hD671QA1Mgh98XYfGQw+z2Iw05xD8QxsWknqkpx+33K9nLTh2LUkBr/+qDHqsaK9H5LPKrJ0raJLVFYtfn3WPLwnOPO0qgzRa4Nnv9ZlCMc9oh5+SBvja+Y+HlL+YTpN6DsCZGpmeI5JRD1hq4wKKxziIiIb1BY5+JryEcyIbBQDlsWoV2zqJLX8q1s1LD9HXwxm+/6NdaiL7gumB9XUP6n/pUT/pHj6p3bcNahmI+89IPH9Yw/5DorcbcvGERJVvzXo30TQRoSn7bf1UpaR85ooRsbWdnMzVCXnihb+QzbM9razAjwEoKzaCwdrNWlTCMKtxxhxowR470WoThmFsjbzvXh8czY8CIfFj/PzQAlhseWfrAygmHuoK9UIj+FkdKcO4pePqX4eivwbnPo2O8LxTmXwEmmYSN/IDWqbfvUw7pOyVp7V+rhOtyzp8WkmfRtU5yaN6EZ0aYQ2V6GKvXH1aV+Kpa92G16Ram7xyLGvvUqref5prnT81AQJgrBUxVL3mdCTQFYV6/6RMsb5/fR8rEjWfRC1+S/vXZ6zcxoKUtJBsPiT28/jH94Bth0UTHcv2T18GbvuOiX2Uh+oLrjq0tVex/6lMa3n/0UfWqn3++bwBjYWsjViNm63Rnnr55/ebRhtCPiG3bXsxndff2/2Hb2pUVJeHbbuu9fYtIHD/eD4ux/Pty2Z4ZFVYpYMS/vt7XszdNT7i33dbrCA4e7D34IfkPh/QMu+nV9W61v5G33V82AFLS/RaPvuAVo2vhhU/AM78IL3wQtp/kwpM+K9TbH+XWt7AobWPgqXqXt83hKy89SUMm6ixkM9FbarJILuoGPvQhc18rIYYJ+Il6/NVIPX6BRa95otalk/fZJQ33d/mWtunLB0OfPkgWzs/HjxEtOUxoz3oT9sGiCsCaEi2ekz6H77JR43K5o8s5fasYSKiRYEI9P1EjJFQsmgeN74Z7/uJFv7obluhF5EeA7wFO5If+xzzL+qIoF4f9jdlMSf8zn9HOfI88ogr+48dfKuYzcduBA0qUw3r9oRc8LMmzqXAW4rewvhFync83U8RPJj0JW24/BN3HCy8ocZugz8Lt1rTG1mnEb2kEEwxa/f/GRm/EWOe6w4f7fgHWSAh0/TbGdqhRMCNnWBlg73lYzmfPm0FxMRSiL7gods7B078Oz/wSnPp9iCfoh/EsYw0thcstZx1AyJPanHr7KUKsNIRuzXeSX3Cequux/6B59aje+XCcr+XVhw18fJ1D/LUaHlKjpW45Lx/bXnCXGhYT5bqZiuTiTN9bSrpuqSFko8JK8JKAs9rg3G/AOfrSvkzgJrRbqPwtfE9OUdCvP5khk1MdEV3zIpVQwYGvgDd950W/qhud6DdSSv/PV/K6cnG4cTCfq3DvoYd64j92TMPpZ8/2oXSrg7fyuiNHdtfrp9R7ycOJfDH2Hf5gd5Mc8/Shz6Nb+uDuu5X077hDSXg+1zWdONGTr0UeLEVgync7jpG+RR9s6IwJAi0yYMS/tra7g59FMsxDH86wH/bCH4oXh+mOO+4oRF9wlXHy8/D0L8Fz74b1L6Bq/r3ggUPACOpcQ24DaUxRLqknMpfzVS7nuGPSEHxqgUyC5FC2NZeJsRfBLUrRfK7dH2vqoB7pGtyIRVvaRcOeqMdwVa6BzyHzlD3+aOH+OFD0mzo+q+wl9RqBrqVv0+t78hdYaBcIee5Ats6TefQm6MsevM2tF9QQmL4e3vr3L/rVXJV59AUF1wJ1DW98o96+5Vs0lP/gg31nvmPH9LFz53bPhj95sifTw4eV+M3TN3Gd933zHAtp2zz3c+d6L3xI+jGqgXH8eN/j/7WvhbvuUk//DW9QY/7UKa3btz79VnJ3++163PlciX19nUX9vwn9Xvc6Pc5wzOzmZq9TGNbvD/Pt02nfO8AMiyH522dj6QkzHAoKrhpu/0Nw+w/B1/wQzLfguQ/Bkz8PJz4K7fP03n4HnNK7cwFWgYl6+1TZ269zTj3XzLeJRXc5U85LnfP7ZHFazpkncr1/pwRrRAvqnfsdHTnb5Bw8OSxfjzQnvjBAOkgz3Sa2WUxXQ7CSPq8h/jiHdgZxQ1MAoNv53BsgOahXs1eSUwdxxiLc77MIkFb1DNB7+SbkS17fg4NFS2IX9HN4tcbUXg9kj/5vA+eB+4F/mFI683KvK17AjY+2VYJ/+GEl/Yce0vD+Cy9oGHxjo28YI9Ln448cUeI3MZ61ih32xrdQt+X1LSRvRsFwWp/1lI9R93/XXert33mnEr/3ms9/4YVewW9d/oy0rX+/zZiH3dEA7/t58k3Te+jDoT426MbC8sOIwTBVYLPst7bU6ChivIJXDaefUNJ/7teyt3/uAhvWqKhvCqMxWCe7GLKHLeptW/laqNHQeWChlk+xF89ljZvm9JueLK0ZjqvY1egmmACv0nI+N2HRzS8C5JK9lNMGDBraJIC5RgDanOdftNrMef5geoSRLi42ea15f6Zh8DX9tEF6ER/Zo7eGPeJg5cvgD/+fL/rx7+vQvYh8EHjNHk/9IPBx4CT68f5z4O6U0t+5wH6+F/hegHvuuedrnn766Wuz4IJXHW2rHvZDD/UT94z0bYjLXqRvIrvhxD1TpVt43zxeK5drmp6AbepdXfdlaxa2n0yU6F//evX4b7tNX3P+vHr6p08ruYv0bYFXVnpBn5UaWmOgYZ97G4gzn7MYCGR5fCtBHHbzG5YGDsf0vhzJQyH6gmuE2RY890F48ufg5EehfYG9lfwebdizqv3lFx5uJmiyoC1FFsNv0kjD/8MucjZnXizHnV+TGhZ1/AsBXSZ+EwmGTNCM9BhhwmJYTXKZzHMYP+VywORAWohOBX6ttcDdpi8ntJK6CX2lQBb4pU7TEosURhbeSVb4C/RlehWs3Qtv+8cX/cj3NdFfKkTkXuA9KaWverlty8Xh5kXXKek//LDm9B99VFvzWjMcm3ZnsHy8Cd9MzGdGuHn6RuiW0zcFvEUDTBNg5W6WJ9/e7lvt3nOPhuXvukuPubmpaz1+vK8qMMI/eLAn4uGgm2EjHOuNbwaISD/Ex1oLWxjfjAYr2QtB0yGXOo/+an9PFzjWj/AKxbXlXL4J0HVw7nF48mfgmffC9mPAxgU2XkEJd009Y2+ha5+VqLl95SJHnhvLWJtbG3tLO8hxZzEcDbRZRGdkbJ6zC5p/t0E9i9a9Uz2OH/URhnYOcTMTe8uisVA3z/tMOuc+RZ3WtyD0XD5n7YCpNFoRs9gw2dpgMSLYxg2vvQne/k8u+jHfsEQvInenlJ7P9/9PwB9PKV28awDl4nCrwEj/0Uf7VrxPPqmPnT2rRDvsUmeKdyN968znfd95bzhZD/rctxGtec1WG+99fxwrx1tbU0//DW9Q4l9b030cP67evrWqNe/70CHdr03Ys2oAmwGwvd0L/ayawCIXNunv8OF+gp+p9N/whl6UeCFcB6J/ReLaci7fhNg+C0ffD0/8NJz5dFbyd3tsWAErICtQ5alSu0g/7SZsm3znMzla7/wYc5Mdx6JcL+WSuWjheXIUIde/+6zalyyO8zXaoz/ofb8KVhkQZ9qaN+6wGLHrA4uGN13K5XzzXt0fY05DVOrp+zGkOr+HXCVAy6Kb38qXw33/80U/1htZjPd/F5GvRm2cp4D//XVdTcG+gveaL7/7bvimb1JF/KOPqqf/8MParMfK4zY3lSjncxXSWXj/0CENu6+u6vm8uam5dsuDWzTACH02UyGgiQFXV/vX33573zjn4Yf1ZmK+e+6BL/sy/du2SvgvvKAh/hMnepW9jdy1kD2oQQJ9Z76trV6ncPasNiGyaoHbbuuJf3l6XkHBvsDkELz52/XWNXDyM/Cln4QXPgQ7T9N36WuAs5DOwtzBfAqswGglt7atcqleVul3MyXbLufifcWihzxOSd/FTO6CjtPNtf4LjzrmYTRzVAyIkn4c6XqCh8aDO6/79ZWG+asD4G7X18cG2o1M6Jn4Q04NSMo2TaOpgHauo3qbLWU555X0bSaATDVNEV6ml/XLYF979JeL4gXc2ohRvefPfU5J34buvPiiCufMA7cUnwnbhqRv3nHX7c6TG/laqZzlyW34zl136X3n1BOfzXoNwXisqnkj/Tvv1DUY6VvaYZn0h9P+oNcaGOmfO6fGix3HSP8bvxFes5f6ZYDr4NH/bV6BuLacy7cQUoLzx+CpX4Jn3wnnHwHOXmDjid78gax8r1k0rfFeRX2RnNvPhGwes+SGPa6DNufwpRpYxrn3vJXNYaI+oZ+cV2uov8rd8cTnEj6vj4c8K4CcaogbSv5Wvx+t7A4057+jx22zsWJzAWIWI66+Cb72Ry/68d2wofvLRbk4FBhiVO/7kUd6MZ+F90+f3p3TH5L+gQNK+nbfhH6Ws7fcv3O9yt1y5JYCMKPBOvft7KiOwIbw3Hmnhvbf+Eb1+r3vh+/YuixqYLn94VAcI3+rEDDSNzHgt32bGh4Xw9Um+qshri3C2gIA5pvw7AfhqZ+FUx/L5Xt7CfpyiN+tKQlXuWFPcr2oZtGFb0DWfqSle5Lz6uS8WSSL47K3T9SQO2QPPSvhRZTw3URTCxbqF9c3zHEOXK7pp877a3S0cHdO97sQ7/n8/ipNK3Q5T5d2YHwPfP2PX/TjKkRfUEBP+o8+2k/ae/JJDZ0b6VtOf0j6Bw8qaR84sLvUzUjf0gBWP28Nerqu7+x32219Xftspt7++nrfOOfwYU1BvPGN6vFPJrqu48eVvK0E0Ajf9mVT8CzVYAI/y9Hv1/K6SxXXlnO5AMgh/gfg8Z+B4x+E7S+x9yAej7blnWqI31ujHOvCh5beRSP+kHPyg2l91nff8vfD6XYxAU2fY48tLHrh51y+G2tP/hBYTLeD7PWL1vH7PLQnJlXvt1vQnM0le00v/IutpgsmXw5/5Icu+hHdyDn6goKrBufUi77zTviGb9hN+g89pOH948c1DG6kf/asGgHPPadkPiT9lZVehHf+fN905+DBnvQtfP/MM31Zn7W9PXy4F9itr2vU4dFHlcRvvx3e9CYN8b/1rboGKyc8fVr3ZaF9GwA0m/WkX9dK9pdSYvdqYSiuBf4y8PD1XE/BDQRfwV1/TG8pwfln4el3wtFfhbMP0Yf4O7Rb3zrMQEP8YwiHlFhDrXl9yWExyQr8Zid74lkRvwjPZ2/fcvgO3R9kj94U801ukrOlSvvmbD7eOHv0q8q2qdKcfHs+RwCcGhl+FUaHcz/+DpoN6M5r7r5rtanPFaB49AW3PIae/kMPaU7/iSfUoz51qm+sY2p4m2N/4IASspF+CD25WvjeRH5tq/sxJb3Vvh85omS9ttb36D93TrcFfc468r3pTbr9+fN9ZUHT9BEBMyIsrP8VX6Hruhhe5Rz9TwNfzUBcOyD+PVHO5YKXxc45OPab8MTPwYnfQ6s391Lxj4AV9bZdrc1yfG5q45x62zFqyN/R592rcc7pV+phSy6Xi+R2ttmatoY4KbLI8xOzqC5mwp/qrV7rS/tSh4rzqmxsjPO0vjGLlr2ju+AP7tlCZoESui8ouEQY6X/uc+rpD0v2Tp/ua+zttLGOegcOKAmbt27z662Nrc23H432Jv2q6jv6reZOmrOZkv7mJruG79x9N9x7rwrt1tfVGDlzRvfnvRoNa2vwtV+r67oYSsOcgpsK7QxevF9L9078Duw8xd4h/oAO4ZloiL+qldSj11D5oukOLEbNWv17yN38nCjxW/07uW//opGPEX6jWgBafZ3IwJOfKOmHqb7WhZy3n+sanYBbhdU3wJsvn+j3UWCvoOD6Yxje/1N/am/SP3lSidVa3p49q7fnn98t5LOmNtbXfmOjz6VbDfyw294LL/RCOzMYTJlv4f3jx/U4jzyiZH733ZrTf8tbdC1nzqhBcvashvxfjugLCm4qhBG87uv11nVw9os6hOf598O5h9GCD1DSPaO3WYBZ9vZHK9DU4FdyPX4usXOtknq3De163/gmZBGejeW1EH9KahQkn3vht4P2ndbWchPaTZid0ePUE/X2wyElfsl9A7o5NNtX9rFc0asLCm5iXCnpW/7cwvurq3qeb231Y2aN9FdXe9K3qMLp07tJ/8gR3dd8rsc7d063eewxJf077lD1/pvepNeUw4ev8wdYUHA94T3c9ofgth8CfgjWn4NnPwDP/hyc+gw6dCeipN8CmzmvPwamGuL3EyXqMMrhe+lFeLHVygDncu37OLfOHeXa/DzYJibUO88d/MSBb3PHvNSvYb6ua5BTWScwhWoK4aAaFVeAQvQFBZeAZdI/daoX8hnpnzrVz563sPu5c+qpm5BvGN4fkr4NubEJfPYc7Cb9gwd70k+pTwOYgfHUU/3Y29e/XlX8BQUFwNpr4a1/W2+zdXjuw/DUL2ov/uYofenejt7a09DWMFuBsKZEHsYa5u9yyYsN1Gm2tRzORuaGcS+yQ0CafspezL3t3TgP82mzwr/T2v6E7qvdgqYCeTEf5PJRiL6g4BXCZr1/4zfuTfpPPaWPWRObIekPPf0jR/qhOzboZmOjH7ZjzXKmUyVzESXzM2f08dVVvR04oB591+l258/rsYY9/wsKCgYYrcEb/6Lemhmc+Aw8/Ytaurf5JSBb2cz11p7JpD/VVrjVWg7dT/tmO1Zzm1qYnQO/mcV1lXrmbpzz/VmpH01J77UaIDkgqfhuMfgm9ZGBK0Ah+oKCK8CFSN8G7jzxhHrjp09ruH1I+i++qB78kPQtp761pbe6VtIfj5XcU9J9iOj+zp/vSd8MiLW1vnFPQUHBy6AawWv/hN66Ds5/EZ75VTj2X+Ds59BcPixIPwHz4yxC/PWB3A0ve/zWHz/l5jpd1Nw+mfTdVHP7YcKC2LtM5NZoR3K73JTr+d2VtcAtRF9QcJVwMdL/3Od25/TPn38p6Vt5nA3dWVnR687mppL5ZNIr+J3rJ92l1JO+90r6k8n1/jQKCm5AeA+H/xAc/gF42/fD5gvw7Pvg2V/SnvycYNEWly29zU8CY/X2R4eyUG+qoXvoe1Z3SdX0qYHmvCrszTioVnJb3FabA6XNrPivVB/gC9EXFOw7XIj0P/1p+MIX+o58JuSbzZSoz5/XnP5k0jfOOXSoV+/H2Iv4rEGPiBoEJupdX9cUwHx+vT+FgoIbGCKweje85e/obecsPPfb8My74PjvQnsU9fJhkdefnUbr9acQVpSgq9wJTzJZxzbXz2cxX7ORW/UGJXw/AVlBS/ai9r5vzr9kea8EhegLCq4x9iL9Rx5RT/9ipH/unJbTmSr/jjv68H7X6bZG9kb+NoinbQvRFxRcVYwPwZv+st7m23Dy0/D0L8OLH4StJ4HNvOFMb4u8/gRkFUZG+FMV4XmPNtSRHKJvoMslf36guvdrMHmZoRUvg0L0BQWvIoz0v+mbdrfh/cxn4POfVyGf9d43r3x9XW8nTyqpr61pnf7Bg+rtd91uT98a86yuXuc3W1Bws6KewGu/Xm9dC+ceg6feCc+/F859HjiXN7S8/jnY8WhL3hUYZa+9yh5/zBP3RPLkvAbi+T7EX11ZQ4xC9AUF1wkX6r1/IdJvGvX019f1ceuid/vtvafftvr8aKTb3Hvv9X6XBQU3OXyAI2/VW/xBWD8Kx94Lz/4qnHoQHdho3fM29DZzwAh2VmF0IOf1VzUfL3lyHq0O2YmdDru5AuwLoheR/w74EeAtwNemlO4fPPePge9GP6X/Q0rpN67LIgsKriFejvSffnr3aN35XEP758/3pD/09A8eVLIvKCh4FeEcHLwHDv5deOvfha0TcOxD8MyvwMlPQPcckMvn2Nbb7CSa159ojt6t5FG7B3JnvlxqdwXYF0SPTrH6b4F/P3xQRN4KfDvwlcBrgQ+KyB9I6QrfdUHBPsalkP5wtO583gv5LKd/4ICW9r3tbdf73RQU3MKY3gFv/na9zTaV7J/8RTjxYdh+BlXuJxZivuYMquAfaW6+mmg5Xn37FS1jXxB9SulzACKy/NS3AT+fUpoBT4rI48DXAh97dVdYUHB9cCHSf+CBPrx/8mQ/Zc964q+v6/MFBQX7BKMVeN2f1lvXwMmH4Olfhed/AzY/j47XhQXpd+e0Ax9jLb27AuwLor8IXgd8fPD/o/mxgoJbDnuR/iOPaEe+5fD+1pYOuykoKNiH8BXc9TV6i/8Uzn8Jnn03HHsfnH4IOI1mqxu97Tx6RYd71YheRD4IvGaPp34wpfRrV2H/3wt8L8A95QpXcJNjSPrf+I096T/wgA65eeopHW5TUFCwz+EcHHozHPqH8FX/A2y+qMN3jr0LTn4K4gtoDv/y8aoRfUrpz13Gy44Bbxj8//X5sb32/xPAT4DOsL6MYxUU3JC4EOn/0T96vVdWUFDwiiACq6+Bt/wtvc3OaXOe7bNXtNv9Hrp/N/CzIvKjqBjvzcAnru+SCgr2L4akX1BQcINjdBDe8C1XvJsry/BfJYjIXxaRo8DXAe8Vkd8ASCk9Avwi8CjwfuDvF8V9QUFBQUHBpWNfePQppXcB77rAc/8C+Bev7ooKCgoKCgpuDuwLj76goKCgoKDg2kBSuvl0ayJyAnj6ZTa7He1NuJ9Q1nRpKGt6eVzqer4spXTHtV7M5eISz2W4cT//VxNlTZeGG3VNFzyXb0qivxSIyP0ppfuu9zqGKGu6NJQ1vTz223quNfbb+91v64GypkvFzbimErovKCgoKCi4iVGIvqCgoKCg4CbGrUz0P3G9F7AHypouDWVNL4/9tp5rjf32fvfbeqCs6VJx063pls3RFxQUFBQU3Aq4lT36goKCgoKCmx43PdGLyDeLyBdE5HER+YE9nh+JyC/k539fRO7dB2v6H0TkURF5SEQ+JCJfdr3XNNjur4hIEpFrqkq9lPWIyF/Ln9MjIvKz13I9l7ImEblHRH5bRD6Tv7sr71358mv6TyJyXEQevsDzIiL/r7zmh0Tkhu2AX87lq7OmwXavyrl8qWu61c/na3oup5Ru2hvggS8BbwJq4EHgrUvb/D3g3+X73w78wj5Y058Gpvn+390Pa8rbrQEfQUcH33edP6M3A58BDuf/33m9PyM0j/Z38/23Ak9dyzXl43wD8EeBhy/w/LcA7wME+BPA71/rNV3Hz7+cy/vsXH4Fn9Mtfz5fy3P5ZvfovxZ4PKX0REppDvw88G1L23wb8JP5/i8Df1ZE5HquKaX02ymlrfzfj6NT+64lLuVzAvjnwL8CdvbBer4H+LGU0hmAlNLxfbCmBBzI9w8Cz13jNZFS+gg6vPpC+Dbgp5Li48AhEbn7Wq/rGqCcy1dpTRmv1rl8qWu65c/na3ku3+xE/zrg2cH/j+bH9twmpdQC54DbrvOahvhu1Iq7lnjZNeUw0RtSSu+9xmu5pPUAfwD4AyLyuyLycRH55n2wph8B/qbogKZfB/77a7ymS8Er/b3tV5Rz+dKw387lS1oT5Xy+FFz2ubwvhtoU7A0R+ZvAfcA3Xud1OOBHgb99PdexhICG+74J9ZI+IiJ/OKV09jqu6TuA/5xS+l9E5OuAnxaRr0opxeu4poJ9gHIuvyzK+XwNcbN79MeANwz+//r82J7biEhAQzSnrvOaEJE/B/wg8K0ppdk1XM+lrGkN+CrgwyLyFJofevc1FPFcymd0FHh3SqlJKT0JPIZeKK4VLmVN342OVSal9DFgjPaovp64pN/bDYByLl+dNb3a5/KlrAnK+XwpuPxz+VqKC673DbUSnwDeSC+4+Mqlbf4+uwU8v7gP1vRHUKHIm/fL57S0/Ye5tmK8S/mMvhn4yXz/djSkddt1XtP7gL+d778FzenJq/D93cuFBTz/DbsFPJ94NX5T1+nzL+fyPjuXX8HnVM7ndO3O5Wv+w7veN1Sp+Fg+2X4wP/bPUOsa1Er7JeBx4BPAm/bBmj4IvAg8kG/vvt5rWtr21bg4vNxnJGgI8lHgs8C3X+/PCFXm/m6+aDwA/PlXYU0/BzwPNKhX9N3A9wHfN/icfiyv+bPX+nu7zp9/OZcvYU1L217zc/kSP6db/ny+ludy6YxXUFBQUFBwE+Nmz9EXFBQUFBTc0ihEX1BQUFBQcBOjEH1BQUFBQcFNjEL0BQUFBQUFNzEK0RcUFBQUFNzEKERfUFBQUFBwE6MQfUFBQUFBwU2MQvQFlwwRuVdEtkXkgcFjnYg8kGdIPygi/zD3076c/R8Skb+3dLyXzGYWkUk+5lxErneL2YKCGxLlfL51UIi+4JXiSymlrx78fzul9NUppa8E/ivgvwZ++DL3fQidKX5RpJS28xqu+RjYgoKbHOV8vgVQiL5gF0Tku0TkUyLykIh89JW8NukM6e8F/oEo/qaIfCJb6/9eRHw+xr0i8nkR+RkR+ZyI/LKITIF/CXx53v7/kXfrReQ/ZA/jAyIyuapvuKDgJkY5nwugEH3BACKyBnw/8HUppbcBf+GV7iOl9ATggW8A/jrw9dla74C/Mdj0DwI/nlJ6C3Aetfx/gOxhpJT+L3m7NwM/lj2Ms8BfuYy3VlBwy6GczwWGQvQFQ3TABPhfROS+dGWzoL8J+BrgkzkH+GeBNw2efzal9Lv5/juAP3mB/TyZUnog3/8UOt2poKDg5VHO5wJAR/UVFACQUtoSka8C/iLwEyLyH1NKP/5K9iEib0IvMKfRsZP/+EKHe5n/G4bzu+3CVVBQ8DIo53OBoXj0BQuIyJtTSpsppZ8H3oOO/Xwlr78D+HfAvwU+BPxVEbkzP3dERL5ssPk9IvJ1+f53Ah8F1oG1K3wbBQUFlPO5oEfx6AuG+MF8sm4CjwDfcwmvmeRQXgW0wE8DP5pSiiLyfwU+kMtzGuDvA0/n130B+Psi8p/QGdT/a/ZAfjeX4LwPnb1cUFBweSjncwFAmUdfcOkQkXuB96SUvmqf7Ocp4L6U0skr2U9Bwa2Icj7fOiih+4JXgg44OGywcT1gDTZQryNez7UUFNzAKOfzLYLi0RcUFBQUFNzEKB59QUFBQUHBTYxC9AUFBQUFBTcxCtEXFBQUFBTcxChEX1BQUFBQcBOjEH1BQUFBQcFNjEL0BQUFBQUFNzEK0RcUFBQUFNzEKERfUFBQUFBwE+P/D4XzVhkC1UHFAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 576x144 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Trajectories in the depth domain (we can now use the actual `t_span`, since only points in the span are given by the model)\n",
    "plot_2D_depth_trajectory(t_span, trajectory, yn, len(X))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "e5b630a2",
   "metadata": {
    "papermill": {
     "duration": null,
     "end_time": null,
     "exception": null,
     "start_time": null,
     "status": "pending"
    },
    "scrolled": true,
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 216x216 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Trajectories in the state-space\n",
    "plot_2D_state_space(trajectory, yn, len(X))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "b9b78a7b",
   "metadata": {
    "papermill": {
     "duration": null,
     "end_time": null,
     "exception": null,
     "start_time": null,
     "status": "pending"
    },
    "scrolled": true,
    "tags": []
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/michael/.cache/pypoetry/virtualenvs/torchdyn-voYSR01p-py3.8/lib/python3.8/site-packages/mpl_toolkits/mplot3d/proj3d.py:136: VisibleDeprecationWarning: Creating an ndarray from ragged nested sequences (which is a list-or-tuple of lists-or-tuples-or ndarrays with different lengths or shapes) is deprecated. If you meant to do this, you must specify 'dtype=object' when creating the ndarray\n",
      "  return np.array([xs, ys, zs, np.ones_like(xs)])\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x216 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Trajectories in space-depth\n",
    "plot_2D_space_depth(t_span, trajectory, yn, len(X))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "35e0a300",
   "metadata": {
    "papermill": {
     "duration": null,
     "end_time": null,
     "exception": null,
     "start_time": null,
     "status": "pending"
    },
    "tags": []
   },
   "source": [
    "## Stacked Neural ODE (aka Piece-wise constant parameters)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c045cac2",
   "metadata": {
    "papermill": {
     "duration": null,
     "end_time": null,
     "exception": null,
     "start_time": null,
     "status": "pending"
    },
    "tags": []
   },
   "source": [
    "While looking for an \"easier\" solution than Galererkin Neural ODEs without trading the expressivity of the model, **stacked neural ODEs** may come in handy. Instead of approximating the solution of an infinite-dimensional problem (e.g. Galerkin-style), we can also use piece-wise constant weight functions. Let us subdivide the depth in $N$ intervals\n",
    "    \n",
    "$$\n",
    "        \\mathcal{T} = \\prod_{i=0}^{N}[t_i,t_{i+1}], \\quad t_0 = 0, \\quad t_{N+1}=T  \\quad(\\forall i  \\quad s_i\\leq t_{i+1})\n",
    "$$\n",
    "\n",
    "We can then define the weights as piece-wise constant functions \n",
    "\n",
    "$$\n",
    "        \\forall i  \\quad t\\in[t_i,t_{i+1}]\\Rightarrow\\theta(t) = \\theta_i, \\quad\\theta_i\\in\\{\\theta_1,\\theta_2,\\theta_N\\}\n",
    "$$\n",
    "    \n",
    "The solution of the neural ODE becomes \n",
    "    \n",
    "$$\n",
    "    \\begin{aligned}\n",
    "        z(t) &= x + \\int_0^S f(z(\\tau),\\theta(\\tau))d\\tau \\\\\n",
    "        &= x + \\sum_{i=1}^{N-1}\\int_{t_i}^{t_{i+1}} f(z(\\tau),\\theta_i)d\\tau\n",
    "    \\end{aligned}\n",
    "$$\n",
    "    \n",
    "This is equivalent to stacking $N-1$ neural ODEs with **identical structure** and **disentangled weights**\n",
    "    \n",
    "$$\n",
    "        \\begin{aligned}\n",
    "         \\dot z =  f( z(t),\\theta_i) \\quad t\\in[t_i,t_{i+1}]\n",
    "        \\end{aligned}\n",
    "$$\n",
    "    \n",
    "which are **stacked sequentially** and trained with *classic* adjoint method.\n",
    "\n",
    "In principle, $f$ can be chosen arbitrarily. Hereafter we consider, e.g. the `data-controlled` case.\n",
    "\n",
    "**NOTE:** Let $\\Delta t_i = t_{i+1} - t_i$. Since the individual Neural ODEs are *depth-invariant*, we can just solve the ODEs in $[0,\\Delta t_i]$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "6042b458",
   "metadata": {
    "papermill": {
     "duration": null,
     "end_time": null,
     "exception": null,
     "start_time": null,
     "status": "pending"
    },
    "tags": []
   },
   "outputs": [],
   "source": [
    "# We choose to divide the domain [0,1] in num_pieces=5 intervals\n",
    "num_pieces = 5\n",
    "\n",
    "# Stacked depth-invariant Neural ODEs aka Neural ODEs with piecewise constant weights \n",
    "nde = []\n",
    "for i in range(num_pieces):\n",
    "    nde.append(NeuralODE(nn.Sequential(DataControl(),\n",
    "                                      nn.Linear(4, 4), \n",
    "                                      nn.Tanh(), \n",
    "                                      nn.Linear(4, 2)), solver='rk4')) \n",
    "pc_node = nn.Sequential(*nde).to(device)\n",
    "\n",
    "t_span = torch.linspace(0, 1, 5) # here we chose Δt_𝑖 = 1 ∀𝑖. \n",
    "\n",
    "# we need a little wrapper to handle the `t_eval` outputs\n",
    "class PC_NeuralODE(nn.Module):\n",
    "    def __init__(self):\n",
    "        super().__init__()\n",
    "        self.pc_node = pc_node\n",
    "    def forward(self, x, t_span):\n",
    "        for node in self.pc_node:\n",
    "            t_eval, traj = node(x, t_span)\n",
    "            x = traj[-1]\n",
    "        return t_eval, traj    \n",
    "    \n",
    "model = PC_NeuralODE()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "68be7807",
   "metadata": {
    "papermill": {
     "duration": null,
     "end_time": null,
     "exception": null,
     "start_time": null,
     "status": "pending"
    },
    "tags": []
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "GPU available: True, used: False\n",
      "TPU available: False, using: 0 TPU cores\n",
      "\n",
      "  | Name  | Type         | Params\n",
      "---------------------------------------\n",
      "0 | model | PC_NeuralODE | 150   \n",
      "---------------------------------------\n",
      "150       Trainable params\n",
      "0         Non-trainable params\n",
      "150       Total params\n",
      "0.001     Total estimated model params size (MB)\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "6c4ad0c282b048d692e41ff9c7d07add",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Training: 0it [00:00, ?it/s]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "learn = Learner(t_span, model)\n",
    "if dry_run: trainer = pl.Trainer(min_epochs=1, max_epochs=1)\n",
    "else: trainer = pl.Trainer(min_epochs=250, max_epochs=250)\n",
    "trainer.fit(learn)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "25860e53",
   "metadata": {
    "papermill": {
     "duration": null,
     "end_time": null,
     "exception": null,
     "start_time": null,
     "status": "pending"
    },
    "tags": []
   },
   "source": [
    "**Plots**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "id": "7be6d46e",
   "metadata": {
    "papermill": {
     "duration": null,
     "end_time": null,
     "exception": null,
     "start_time": null,
     "status": "pending"
    },
    "tags": []
   },
   "outputs": [],
   "source": [
    "# Evaluate the data trajectories\n",
    "t_span = torch.linspace(0,1,5)\n",
    "trajectory = [pc_node[0].trajectory(X_train.cpu(), t_span)]\n",
    "for i in range(1, num_pieces):\n",
    "    trajectory.append(pc_node[i].trajectory(trajectory[-1][-1], t_span))\n",
    "                      \n",
    "trajectory = torch.cat(trajectory, 0).detach().cpu() \n",
    "tot_t_span = torch.linspace(0, 5, 25)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "id": "f7e6fadd",
   "metadata": {
    "papermill": {
     "duration": null,
     "end_time": null,
     "exception": null,
     "start_time": null,
     "status": "pending"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x144 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Trajectories in the depth domain\n",
    "plot_2D_depth_trajectory(tot_t_span, trajectory, yn, len(X))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "id": "f63c764e",
   "metadata": {
    "papermill": {
     "duration": null,
     "end_time": null,
     "exception": null,
     "start_time": null,
     "status": "pending"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 216x216 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Trajectories in the state-space\n",
    "plot_2D_state_space(trajectory, yn, len(X))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "id": "76c59811",
   "metadata": {
    "papermill": {
     "duration": null,
     "end_time": null,
     "exception": null,
     "start_time": null,
     "status": "pending"
    },
    "tags": []
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/michael/.cache/pypoetry/virtualenvs/torchdyn-voYSR01p-py3.8/lib/python3.8/site-packages/mpl_toolkits/mplot3d/proj3d.py:136: VisibleDeprecationWarning: Creating an ndarray from ragged nested sequences (which is a list-or-tuple of lists-or-tuples-or ndarrays with different lengths or shapes) is deprecated. If you meant to do this, you must specify 'dtype=object' when creating the ndarray\n",
      "  return np.array([xs, ys, zs, np.ones_like(xs)])\n"
     ]
    },
    {
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\n",
      "text/plain": [
       "<Figure size 432x216 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Trajectories in space-depth\n",
    "plot_2D_space_depth(tot_t_span, trajectory, yn, len(X))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3aff8bd9",
   "metadata": {
    "papermill": {
     "duration": null,
     "end_time": null,
     "exception": null,
     "start_time": null,
     "status": "pending"
    },
    "tags": []
   },
   "source": [
    "## Stacked Neural ODEs with Discrete State Transitions\n",
    "\n",
    "These are basically the `Stacked` model where, at the end of an interval $[t_i, t_{i+1}]$, the state is also updated by learned transition maps $g(h, \\omega_i)$ parametrized by a NN, i.e.\n",
    "\n",
    "$$\n",
    "  \\left\\{\n",
    "        \\begin{aligned}\n",
    "             \\dot z &=  f(z(t),\\theta_i) \\quad t\\in[t_i,t_{i+1}]\\\\\n",
    "             z^+ &= g(z(t),\\omega_i) \\quad t = t_{i+1}\n",
    "        \\end{aligned}\n",
    "  \\right.\n",
    "$$\n",
    "\n",
    "**NOTE:** While not standard, this class highlights how Neural ODE variants can be put together easily via torchdyn's API."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "id": "82e3f1f6",
   "metadata": {
    "papermill": {
     "duration": null,
     "end_time": null,
     "exception": null,
     "start_time": null,
     "status": "pending"
    },
    "tags": []
   },
   "outputs": [],
   "source": [
    "# We choose to divide the domain [0,1] in num_pieces=5 intervals\n",
    "num_pieces = 5\n",
    "\n",
    "# stacked depth-invariant Neural ODEs\n",
    "nde = []\n",
    "for i in range(num_pieces):\n",
    "    nde.append(NeuralODE(nn.Sequential(DataControl(),\n",
    "                                      nn.Linear(4, 4), \n",
    "                                      nn.Tanh(), \n",
    "                                      nn.Linear(4, 2)), solver='rk4'))\n",
    "\n",
    "    # In this case the state \"jump\" is parametrized by a simple linear layer   \n",
    "jumps = []\n",
    "for i in range(num_pieces):\n",
    "    jumps.append(\n",
    "        nn.Linear(2, 2)\n",
    "    )\n",
    "    \n",
    "flows = nn.Sequential(*nde).to(device)\n",
    "jumps = nn.Sequential(*jumps).to(device)\n",
    "\n",
    "t_span = torch.linspace(0, 1, 5)\n",
    "\n",
    "# we need a little wrapper to handle the `t_eval` outputs\n",
    "class PCDST_NeuralODE(nn.Module):\n",
    "    def __init__(self):\n",
    "        super().__init__()\n",
    "        self.flows = flows\n",
    "        self.jumps = jumps\n",
    "    def forward(self, x, t_span):\n",
    "        for k, node in enumerate(self.flows):\n",
    "            t_eval, traj = node(x, t_span)\n",
    "            x = self.jumps[k](traj[-1])\n",
    "        return t_eval, traj    \n",
    "    \n",
    "model = PCDST_NeuralODE()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "id": "f79a1bf6",
   "metadata": {
    "papermill": {
     "duration": null,
     "end_time": null,
     "exception": null,
     "start_time": null,
     "status": "pending"
    },
    "tags": []
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "GPU available: True, used: False\n",
      "TPU available: False, using: 0 TPU cores\n",
      "/home/michael/.cache/pypoetry/virtualenvs/torchdyn-voYSR01p-py3.8/lib/python3.8/site-packages/pytorch_lightning/utilities/distributed.py:69: UserWarning: GPU available but not used. Set the gpus flag in your trainer `Trainer(gpus=1)` or script `--gpus=1`.\n",
      "  warnings.warn(*args, **kwargs)\n",
      "\n",
      "  | Name  | Type            | Params\n",
      "------------------------------------------\n",
      "0 | model | PCDST_NeuralODE | 180   \n",
      "------------------------------------------\n",
      "180       Trainable params\n",
      "0         Non-trainable params\n",
      "180       Total params\n",
      "0.001     Total estimated model params size (MB)\n",
      "/home/michael/.cache/pypoetry/virtualenvs/torchdyn-voYSR01p-py3.8/lib/python3.8/site-packages/pytorch_lightning/utilities/distributed.py:69: UserWarning: The dataloader, train dataloader, does not have many workers which may be a bottleneck. Consider increasing the value of the `num_workers` argument` (try 48 which is the number of cpus on this machine) in the `DataLoader` init to improve performance.\n",
      "  warnings.warn(*args, **kwargs)\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "91289b3893174181a11ea6425fdfb711",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Training: 0it [00:00, ?it/s]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "learn = Learner(t_span, model)\n",
    "if dry_run: trainer = pl.Trainer(min_epochs=1, max_epochs=1)\n",
    "else: trainer = pl.Trainer(min_epochs=200, max_epochs=250)\n",
    "trainer.fit(learn)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "341dd04f",
   "metadata": {
    "papermill": {
     "duration": null,
     "end_time": null,
     "exception": null,
     "start_time": null,
     "status": "pending"
    },
    "tags": []
   },
   "source": [
    "**Plots**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "id": "ff879e79",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Evaluate the data trajectories\n",
    "t_span = torch.linspace(0,1,5)\n",
    "trajectory = [flows[0].trajectory(X_train.cpu(), t_span)]\n",
    "for i in range(1, num_pieces):\n",
    "    post_jump = jumps[i-1](trajectory[i-1][-1]) # apply jump to last solution point\n",
    "    trajectory.append(\n",
    "        flows[i].trajectory(post_jump.cpu(), t_span))\n",
    "                      \n",
    "trajectory = torch.cat(trajectory, 0).detach().cpu() \n",
    "tot_t_span = torch.linspace(0, 5, 25)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "id": "1b4374dc",
   "metadata": {
    "papermill": {
     "duration": null,
     "end_time": null,
     "exception": null,
     "start_time": null,
     "status": "pending"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x144 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Trajectories in the depth domain\n",
    "plot_2D_depth_trajectory(tot_t_span, trajectory, yn, len(X))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "id": "df07d95a",
   "metadata": {
    "papermill": {
     "duration": null,
     "end_time": null,
     "exception": null,
     "start_time": null,
     "status": "pending"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 216x216 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Trajectories in the state-space\n",
    "plot_2D_state_space(trajectory, yn, len(X))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "id": "e9135c14",
   "metadata": {
    "papermill": {
     "duration": null,
     "end_time": null,
     "exception": null,
     "start_time": null,
     "status": "pending"
    },
    "tags": []
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/michael/.cache/pypoetry/virtualenvs/torchdyn-voYSR01p-py3.8/lib/python3.8/site-packages/mpl_toolkits/mplot3d/proj3d.py:136: VisibleDeprecationWarning: Creating an ndarray from ragged nested sequences (which is a list-or-tuple of lists-or-tuples-or ndarrays with different lengths or shapes) is deprecated. If you meant to do this, you must specify 'dtype=object' when creating the ndarray\n",
      "  return np.array([xs, ys, zs, np.ones_like(xs)])\n"
     ]
    },
    {
     "data": {
      "image/png": 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Bfqjaa51zOHNeqDbnwx0TDkfo9nG16yvgTQnzOvFFc0bFRTxIp5QaqJQ6SSk1QCnVQ0Q2AKcBW0RkhohEpLQPPviA3r17k5+fz2OPPRZpdYI4oa21+HEyrg+Ow732vhCBK3Sr3QHwWP3uPcBBDhWMy3ql6eO9nSC9M3jSQaWAKwuMDkAnoA3aPD+cOANhvswIjquLxLXkmisqLuzHhVLKEBET3Wp3BlYBu5VSAqzFstGUUipch1wgEODmm2/mo48+Ii8vj6KiIs4//3z69YvcO+qIPIQVj+Je/2itjRlogQvVw2H19bldaNFmgicL3JlgKDADliNcaQtABAwviGWSSwD9wKhEt/AxIC2n2Yo+cADWrIHFi+G772DjRli3Tm/fvRsamiOlVDjHRD8qLmyRWwJHRH6mlEpD98vzgRxggoiss/aH7WGZN28e+fn59OjRA4ArrriCd999N2KR+/1+Kioq+Oijj8jJyaFnz54RnZ9UVFbgWv90yAa7zw3avD7I4cWdoo/3ZoGRDoZLD2MF0CLHBGWA2wv+ci1sJaDc1eebAZBK61q2ud5CNMInM38+jB4NJSUNH9sUUsLsSYSa7i0qcuviXYGfLJN8vlKqBNgUqYluU1xczFFHHRV8n5eXx7fffnuYMw7l8ccfZ9q0aVRVVdGnjxN0waLbUcFhsUy0uV2OFnh9JqAtbi9422hxu9wQCOh+vUIL3XYGGR7doqtKvU2hxS4C4rIeApbl4PNZ17YfLKrW31Aa6os3NDkmr4H9mnnz4KqrYNOmsA5vEhddBL/9LRQVRXZeNGPbwxJ5iKl+HVCslPoMPSA6Afgn8O+QY1qUO++8kzvvvJOnnnqKzMzM1t2Kl+7D9dM/QzZUUT2EVRcu9NeYCp5sMDK0QJUJdp9Q/LqVVgJGCiAgPh3MglEtfjEsD4/oh4MZ0Oe5UnSQisv+qSmqxRym0SdA1ZoGDlLQvn+dew4cgCefhJdegn37wrtkYykogF//Gq68snmvEwnhtuT2t+IBxgI90L+QNei+OY0ReG5uLps3bw6+37JlSzAlVKQ4fXJg/s9QNYRTX7/Yhf7q07QDzZ1ZLe6AqQVtBrR4DWWJXGkT3ARcLvCmQkAhgXKUGQBDLM0a+n+FfkAgIF7L1IfwPOdQ4wHg2xDG8Zngyq6xpbIS7r8fnn22+pnVGJSCzExIS4PsbN0jaNcOOnSAvDz4n/+B005rfPnNTbgitwU8C3hFRNZG4+JFRUWsXr2a9evXk5uby5QpU3jjjTcaVVZmZiZ79uxp+MBkZc96XKUfN3CQQVDcRoZ2qim3FqXf8mrbLhVDAK8WPlXa2rb74kaaFrl4UP7d4CsHswICft3CKwHlshxzossNDqHZIashbw+HP1ybWiCletqr3w9PPw2vvBKewOfPhy5dID0dPB79HFOquocSC6I1Vh6WyG1nmoh8bl3chfX1NMVEd7vdPPvss5x11lkEAgHGjx9P//51m1wN0epb8m+vOkwbqQia5SoDvNkh4g5oYYrV+hoCpGihSiUEDN2au1Iscacgng6Q2hnlyYbyXUjFdlRgP1SVQqAMET/K9OvzxDLPVehorVT/VaqW0EPe+DdGcAO8kKa7aqYJU6fCX/4CpWGEZT33HBx7bASXSjAaNeIuIpHEOx6W0aNHM3r06CaX06pFvvlL3P7lhzkgE1Sm9pjXEHfA6lODFqLHMtUrdONruMCTooNmvOmIpz2kdwFPB8SdiWl4UK5MVPqRULUPKnZB5XaUv8TyvFutu/gtp1xIleptwa2hOdkawQ0wdP3b5CMCc+bAgw/qYa2GOPZY+MUvIrhUApI0U01bdQqoJdccZme6DmQxvFrMgQAE7AklJlrcbv2/VIKpEEOhUtIAL3iyEE9HVFonSOmEuNNQYqAkoP+6PYjfRFI6IN42KH9XVOVupHIryr8PfGUQqNRmvwJMRbXC67E9GnSy1cYNKW2h0zCWLoV779Vj2OEwf36El2pBWtRcTwRabVjrgjtws6uenR5QbXVrbZqW88sKB1UKcOlWPaBDU8VwozxeFKngzkJSOqFSO0NaR0zlRYlgEEDcXsz0XkjWMQCosrUYZZswfPsRw0BcR0BaJ/CXQsUOqKrdpFrDblYIq2AL34C9/w3bNadJBU9naD+U9VtTuOsuWH44oyaEN9+M6EIJS9KIvFWmZf7vVbj3vVfPTgVkAZZTzVWpt9nDXcoy1wMBcHnASEMZKXoozXsEpHYAT3tMw41CdPfa245ARj6SmQ8p7bVzDZC0owi0PQjlW1GlazAqt6B8paAUpjsNZVrj17ZTz+4e2P5c7d1BNk7DiChSLgOoAl85u34ymfiXvXz9dWfCWXNh2DCwMoInPUkl8lZlrs/+H9yVh7M1s9Hj2H5wiRV6avVdxdT6MtxgZII7FXG1RaV2QdI7aQcbLjAUypOKpOZhZvZE0o/WQS61zUilwJMBnl5IVk8CvhLUwY2o0nWoyq2oQGX1cUBwyoQCUVadvvtfjBqTaMJBf99l5WU8+fbFzJrbicrKBk4B3G7db28tJJXIW4W5XlEBHxXh5nCdzlTrrw8dZopuucW0Zox6dFSbNx1cbSHlSEhph+lyYygPuNMRTxvMzB5I5jGQ0lFHuYWDMsDbBvEORNr01w65QLnlXbfHpBTBB44y4ItbcfNjo27HQV8GLy2byxtfDOJAmGGpH37YqEu1OE6fvBatoiXfsxX1ZSEuDjcuZH+l9lxun2UOu8GdrltiVzp4cyC1E+JKB7cXZaRBSlvMlFzMrHyor9WOBOWqMXZdJ5/ehPvguxEVq5NPDad8xHRmzPDywgwPu+pzS9RizBg4+eSILpfwJI3I3W43gUDURvbijy1fYiwejdFg9IiJjlH3EuzzulLBnQ0p7cDdGUltB65UlCsd5W2DpOYQyDjG6mu3C/a1m51Pb8ZV8s+Gj8MWdhqct0O/N+HjWX6eecZFcXF4l8vIaD3OtlCSRuRJzcp/4Fp3W5heZ2tYTA9067DVlHbg6YKktUN526A87ZHULgQyuiOZvSCtc/jmeLT44ne4Sl5r8DP5Ac47UGObCCxcqHjmmRTWrdO+w3D4+uvGVDR2OOZ6a+HLX+LeE2mor0IPLbWHlC6QngMpuZBxFIHsnkh6Hx3U4opRPrz//gHXvpfrFbgf4NQtOlC8DlatgkmTXKxYoV0U4XDjjXDMMY2pbOKTVCKPdgK8gwe1J9bttrL+tiQiMOsk3IGVEZ7oBdpB6hGQ2RUye2K26YeZ1R+y8sGd1hy1DZ9dm3Hte+EQgfsBevwX+h932NM3b4Znn3Xx5ZfhhawC5OTAM880prKxI6Y53pqbiRMn8vLLL9OpUycAHnnkkYjCXkUkajdowgSDqiqDnBzhiCNMcnLgyCOFdu30rKTMTPB69SuqD4HdxfBVEe7DOthqo9CZXLpAdj+k3bEE2g+G7IGQ2jG2My1CyehAIDjHvTecF37I2U8/wcsvu5g1SxGJj3XRoohrmVTEncgBfvvb33LHHXdEfF5aWhrl5eWkp6c3fHAYfP65jn82DIXH4yIlRWf3SE/XTpysLHvKodCxo5CTI3TuDG3b6gdBWpp+paRUz2xq8GHw/asYa34dYfK9FFCdoN1AzJzhmDnDIbO3HiqLN9LTg86zSCgpgddfN5g+XbF3b/hTR++5Bzp2jPhySUVcirwxVFRUEAgEeP3117nyyivJyspqcpler8mBAwaBgBapYVhTrI1qweqXwuNRuN26VbeFHfowyMiANm3EegAIAwcKhYW1Ljj3QtwHG5ouGooClQNZxxLIHYF0Oguye8RPqx0lKirg3XcVU6YY7NxpJZsJg+7dtcgTkaQ21wGeffZZXn31VQoLC5k0aVKDudSvu+46li9fzrZt29i+fXvUhtKGDNEpguwoquCMTAVVVdVRmqC32dl67L/2w8BlgFKCoQK4jQCG8pGdWsLj173CqadmQb/r4MPjcLMtgtrlQPYgAkedixwxAtLDS32UaPh88PHHismTXWzaFL6jDSDCTGJJi2rhlY4EYMSIEWzffuhCKw8//DBDhw6lY8eOKKW499572bZtG//4xz8OX6jVD7/qqqu49dZbo5brbeVKOPtsN1VVQOVelPhABDFMXIZLi1y58PkEwYWBYSUzNTAQKz2CgbLW81IhCRP8ZNA9Zz1Tb72Avt0iSTbWCWl/EoGjL4ecU6086MlJIADffKOYNMnF/Pna0SZCHbHph3Zunn0WrruuRarZLBiGgccTcXerzuY/Ji35nDADh6+//nrOPffcBo+zTZtoR7316QMdOwbYVgwBUxEQr86GZBqYIihMxFAYhomhTET5MUw9scs0BKWDsxGrI+4LCEoZGGIQQLFmZy+uff6f/PvO0XRu31BMZlfM3HMw8y6GDoNDcqYlJ6YJK1cqXn7ZxeLFOpWxUuGNiR93XGILHKJrrrf0wFCDbNtWbbJOnz6dAQMGhH1utOPXXS4YN05wGT48nkpSPVUYhg+kCkN8YApiguDCb7qp9KfgM1OoFC++QKp+iZeA6cIUA4WhE68EFwhQrNgymKuenkp5eV1RZgrxDMLf7xn8/zMXc/DjkHNC0gtcBDZsgMmTDb7+GsrK6mvBD0Upx0yvTdz9Wv7whz+wZMkSlFJ069aNF198MexzmyN+/Zpr4MUXUtm720ApME3dQRfxo6dRgT/Y41H4MZDQNb/EFTwuOCmjxgu+XHsa5z36Lz6470LcbhBSCXS6EnpeA+0HVXfy0T/2QED7BA4e1H3Wqir9135p34HC79fHpqYK3bpBmzaJ4ZPbtg1ee83Fxx8rDhywkr+adYtcqZq+kddfb7l6JgpxJ/LXXnut0ec2x0y0Tp3g/Av8/P3vXgJ+qI4Jt9bskmqxNoWv1o6k203LuemCT8noexk75qWxf78eOtq/X1FSoqiqAr9f4fNpAds/entYLtTxl5qqPf0ej/b05+cLp5xictxxQk6O3haPgt+zB95+22DmTMWePVrghzPTQwU+fDhcfHHL1DORiInjrbn4y1/+gsfj4aqrropqubt3Q2Ghwe7dcde7qYEdmRf06ruqs46KQG4uFBUJJ5wgHHeccOSRQkZG+Ct7NDclJfDeewavvGKwdm21hWK35PVj4PXq/OrJgtvtbsziCvHjeGsuMjMz2bu3oVU2IqdDB3jySZOf/zy+Re73V4vaNKv/d7m0ab9uHezYoVi2TNGvHwwcKAwcaJKbq8fw09J06x8Lysvhk08UU6carF+vBW6b6A2b6SYzZ8b3dxNLkkrkGRkZFIc77zBCLr4YAgE/kyZZYir5DkUlhhICojCUD7fpw3BV4TZAGQE87iq8bh+pnhLSUgJ43AdJ91bSJvMgbdIO0DazgnZZFaSlwy+fvJF9FNJU0982b+3+uN2y2/vKy7VTa/duWL9esWyZi169TLp3V/ToIXToAJmZQnq6tgyaC79fv7QfwWTpUsXUqW6++656LNw06zbTDaOm8C+80M+wYTF6OiUASSfy5swOc9ll+gXANy/i3vU21VM77UUEavdIPIDLmtOdDp52kNoJM+VIJKM7ktUP0vPY9IcuvDbNz82/Ngh/Le+6sUM+A4HqCTamtfKRiO6nl5bqln33bti61eD776FzZ8jLM+nWDY46SlswGRm6hW9sbH4goIVsC7qiQigvFw4eFMrKtIm9f79i7lwXCxdqgRtGtZlem9oLHmRlBZg8OYDP52vMuHLckvQRb42lRVNAtR8Nu94g6IAD9O106YUI3BmWoI/ATD8aychHsntDeldI6Qzu1FoLDsDV18BJJwvHH+8nWl+N3WLa2JF6WVn6b1mZntm1f7/2aq9bZ7BypZ6I07Wr0KOHFn92tm7dU1Prvxbo6MDyclvMUF4ulJWZlJYq9u2DkhJFWZniwAE3Bw8qDh5UlJfr1Mjl5bpOthVSl8jd7tCwVuGzzwzcbndwBVCjxacLxj9JJ/IWSwHV/Qz4MV03O+5M8LSFtCMw045CMvoibY6B9O46P1odgq6Pnj212Lp0aVjooeZ0JGt9+XwEZ3G5XFpMZWW63753r/ZwFxfDjz8a5OTo1r17d8XRRwvt2x9qzpumiYggIvz4I6xfb1BWpgVdWmpQVubh4EEoL1dUVOgHjT0M6PPp6+7fX22e20Kv6/OGxq3feCP07g1gYBgGVVVVeL1eR+i1SCqRt2judY8Hf/cbUJ5spE1fyOxhtdBpYQu6PjIytBn7t7/5+etfobjYoK64JVsIbrduYV0uLRTb1D3cwEllZbWDzjCE7Gxtjfh8ekqn261ne/30E2zcqPjxR0VOjtC1q8nRRwudOwdo2xbS07U5r81oxbvveikuNjAMLWLbctCtenW3wTbfDaO61bZfdQnc46nZsufkCE89Vf3e7Xbj8/mCZnuiC90x1+uhxXOv9/+jlVK4efjVr/QLTD791OSBB3Tao9p99lCT3OutKfhQQdWmoqI6cEYp6NhRaNtWUVmpxVlWpl8pKbB/v1BcDGvWKDp2dJOXZ9Ctm9C9u6JDB0W7doq0NPj8cz3Xu317fc3KyuoAHtvTbxhatGlp+gElAjt2VNe1tpluz/wLNdPrWvnE5XIRCATw+/14YzVMEIcknchbNGNrMwq8NqedZi+PKyxb5ufOO+GrrxQiNQVvt54uV3VCi9RULebKykNncVVVacHt3w+gSE2FlBQhM1MQMaisFHw+HZjictmBObB9u4u1a+GII7STrnt3IS9PsXq1Fqo9f97r1UJ2ufQ2r7d6Np8O7tHXLi+vux+ulD4vNJ/6hAl1zxG3W2+/308gEGjMOHNSknQibw251wcOhFmzQLdofiZMgG+/rSl4e7isvLxa6GlpWmy1n4NlZdoRZ/eTq6oU5eWKlBRITVW0a1fdKoeWuW8f7NwJ69frySRHHaUfIoGATrlka8w+t6xMn2NH69khuLZFUdd4uNer62TTs6dw99313xvD0I64qqoqUlJSEt5sjwZxcQfeeust+vfvj2EYLFiwoMa+Rx99lPz8fHr37s2HDWTFtzPDtCaKimD2bG1Ov/WWn2OP9VO9nLymqkr38ffurX8+dkmJFqIWtt5mO+J++knvS03VmXDS07WQ9+7VTsLNm2HtWvjmG/0AqKzUQ3M7dmgH3rZt+v/du3Wrbcfc2+a77VCr3Yp7PNYCp0HfgvDFFw3fE8OodsSZ4cxqiUOSrk8+YMAA3nnnHW688cYa27/77jumTJnCypUr2bp1KyNGjGDVqlX1mmGGYdDCYboxx/4Riwinnx7gjDP0j+OVV+CvfzXYssVLaIDN4aZq/vSTFnJ2tm5BbfPZFm5paXXmmzZtarbQpaU1o9A2btT9cqiZDNPOriOitymlRR/aWkN1aG7oQ+nPf643geshGIYR7J+73e6EatGjnZA0Lj5537596a3HQmrw7rvvcsUVV5CSkkL37t3Jz89n3rx5hxwnInz77be8/PLLbN68mbFjx7ZEtVsc0zSDP1zbkxwIBAgEAogILpcLt9uN1+vlV7/y8uOPXn76CX79a51yqiFEYPt2PYRmT++0W3bbj1W7dU9Lw/Ky1+w3Hzigz0tPr3aypaRUO9Bs62LXLn29UAxDHxsq8OOOE264Ifx7ZRgGLpcreM9aM3Eh8vooLi7mqKOOCr7Py8urM2xVKcW0adOoqqqiXbt2PP/88y1Zzahjmmbwx2mL2Ra03XK7XC48Hg9er5fU1FRSUlLwer3BVstuudLS4PHHYcsWWLlSGD26OjtNXdhDaPZ4+f791UNdbrcWn8ulBb1/vxbp3r26RQ5Nq2cLvqpKi3Xv3moTftcu/frpJ32N2hNLvN6aw2iGIXz2WeT30Ra67YhrrbSYua6UmtO/f/9Dtj/88MNccMEFTS5/0qRJAPzjH/+gTZs2TS6vpQgNJKnd1VBKYRjGIX8bS7du8NZb2sHVtq0QCNRtFvp82vw2DC04O0ttSkq1x94OorHHwOvy3G/eXD2+bQ+N2Q43O1debcvULru6LGHyZF1OY7AfeD6fr8n3L1FpMZGLyAginGqam5vL5s2bg++3bNlCbm7uYc+x+2LxOHxiC7ouZ5D9Y4yGmBvCMOD77+GYY0JDcmtie7XtCLWysmqzPTUVa6iterab369N+VD27Kk28+1JJfaYd2j/3A6YsYfZQr3/p54Kl1zStM9rh70mSqBMUvbJ6+P8889nypQpVFZWsn79elavXs0JJ5xw2HPiYXXT0L5zVVVVDXNbRIJmZKi57fV68Xg8LRZ/nZsLM2ZAfc9dkWoh2wLVCSy0ePfs0ea3LWx7LL42StVMXhG6GEXo+Llh6DJCHXBpacLMmdH5vLZT1h9J/G+SEBfe9enTp3PLLbewa9cuzjnnHAYNGsSHH35I//79ueyyy+jXrx9ut5vnnnuuwRbaDm3NDtcN20RCzW3TNGs8he0x29CWOZ5akTPP1HnJH3qoukW3h7Vss9k2re2hrtC4c8PQjrXy8voTT/j9Wry2ae7x6Jcd92572u1ottCotunTo/dZQwNlkm3GWkMkVWYYgEsvvZR77rmHHj16RLVc28S2nWK1Tapo9p1bmksvhZkzqz+Py1W9KIQ9WcSOToOaovT7tWA9nupAmFBcLm012Ga6fY4d3qpU9eSYUAfcmDHSLPnaTNPE7/fHdaCMPUrSCJI/MwxEJ+qtIWeYbVLHY+vcGN56C449Vli3Tv9GAoHq1txuxVNStDjt8NPQfHL2A6Auc92OWbfHve0lozIyqsNc167Vpr9NmzbNI3CoGSjTWmasJaXIw+2ThwaSxNoZFmuWL9czu8rKtND37YMjj9Rj4CUlupUV0Ys82hNfKivtbLC6jPpue2qqbs3tPriducb+e+BATTP9k0+a97Mm24y1hkhKkdfVkoc7VGX3+ZP9i6+LH3+EvDzdPxfRQ2AdO+qkEZ06aaebLUh7JlkgUC32+ti0Sa9LVp3uqTqHW1WVfqDYVM8Rb15a04y1pBN5eno6paWlNQJHQmlNrXOktGunV3IdPlwL/cABHZ6ak1Mdt56dXR0IY68PnpFRPcstNOrNprxcB8HYk1Bs8z40XzzobDShc8Sbk3iesRbtIbSkE/m6detYv349Z599dkI7w2JFQQE89RTcfrsW+oYN2qy2Uzd7PNqj3qVLtald09yum3XrtCMvtP/u91c/KHQqp+b9bLWxhzKTPVAm6bzrpaWlnHTSScycOZP29gwJh4gZPx6mTtUtSnq6bsHtcXM7nj01tToSrbwcli6tv18Oh04bDeWuu4R7743yhwgTv9+PiMSNI66ROdehHu960okc4PXXX+fLL78Mhro6NI4TT4Rly/Tvxu2unmxiC9yedGJHwc2bd3iR1yYzU+jcGUaPhscea6YPEQZ28JJhGHHRP2+CM7D1iFxEOPXUU5k0aRJ1xcs7hE+vXrB1a83fTqjI7amnXi8sW3b4sjIzheHDYcQILeyQuUcxxxa6HYkYSxyRh8nChQv5wx/+wHvvvRd1R0ZrorISJk6EadNg+/aa97F2617fuhYZGXpu+ahRwtNPN3uVG40dKOP1emPqiIu2yGPfAWkmCgoK6NatG++9916sq5LQpKTAo4/qgJXp04UhQwSPRz+rbcfb7t36dbjQ1spKvWLL9u0tWPkICZ2xFsuMMtFulJK2JQfYuXMnI0eOZO7cuaSlpbXkpZOa0lJ48EEdKbdzZ3g/yLQ0HVxz553CuHHNXMEmYk9iiVWgjNfrbazQW1dLDpCTk8M111zDM888E+uqJBWZmfDEEzqB4/TpQlGR4HYf/vldXq6zzkyb1kKVbAKGYQRN92QgqVtyAJ/Px9ChQ5k8eTLZ2dnk5OS0dBVaBSUlcP/9MH364Vv37Gx44w3h9NNbsHKNIJb9c6clj4CVK1dy7bXXcuDAAU4//XRmRmtyssMhZGXpIBq7dS8srLt1P3AAHnooBhWMkNDUzi3dP29VSSOaSpcuXZgwYQLff/89J598Mr169Yp1lVoFI0fCZ5/p2PfrrxdycmqK/ZtvFLt2xahyERCL1M7NMRKU9Oa6zZo1axg3bhxz5syJqzjl1sLMmdqc/+47/SO+7johEVwloYEyLZHaWSnVlICc1jVOXhd33nknRx11FOPHj49lNVo1u3fDCy/osNkuXWJdm/BoyUAZR+RNpKSkhJNPPplZs2bRrl27WFbFIcFoKUecYRhNeZC0PsdbbbKysvjd737Ho48+GuuqOCQYoTPWEm3ppVYlcoCrr76apUuX8v3338e6Kg4JhsvlQimVcEJvdSI3DIOnnnqKu+66q9Wtm+bQdBIxtXOrEzlAUVEReXl5vP/++7GuikOCYZvt9hJW0cYZQosi27dvZ9SoUXz88cek2pkIHRzCpLkccU1IxwyO462aiooKNmzYQI8ePRg5ciSPPPJIrKvkkGDEy4y1cGiVIl+9ejX/+Mc/OP300ykpKeGyyy6LdZUcEhB7dZxoCt0x15uB//znP7z++uv8/e9/j3VVHBKQaKeOakJ+N0hEc71bt24ce+yxDBo0iMLCwkP2iwi/+c1vyM/PZ+DAgSxatCjia5xzzjkcOHCAb775JhpVdmhlhDri4nUN9LhPyfzJJ5/QsWPHOvfNmjWL1atXs3r1ar799ltuuukmvv3224iv8ec//5lrr72Wjz76KC6ydTokFqEz1uJxjbX4qk2EvPvuu1xzzTUopRg6dCj79u1j27ZtEZdzzDHHMGzYMF577bVmqKVDayBaM9aao08e1yJXSjFy5EgKCgp46aWXDtlfXFzMUSEpP/Py8iiuL5tgA9x77708//zz7Atds8fBIQJCV2WJJ497XIv8iy++YNGiRcyaNYvnnnuOzz//vNmulZ2dzW9/+1sei2UCcIeExu6f2864eCGuRZ6bmwvoXG1jxoxh3rx5h+zfvHlz8P2WLVuC5zSGa6+9loULF/LDDz80ugyH1o0tdHuNtUhpVeZ6WVkZJSUlwf9nz57NgAEDahxz/vnn8+qrryIifPPNN7Rp04YuTZikbMe1//GPf3Ti2h0aTbwFysStd33Hjh2MGTMG0H2csWPHMmrUKF544QUAfvnLXzJ69GhmzpxJfn4+6enpTJ48ucnXHTJkCJ07d2bWrFmceeaZMV9NwyExcbvd+P3+uFgDvdUHw4RSWVnJ888/z1dffcX777/PCSec4CR/dGg0jQmUaUKmVqgnGCZuW/JY4PF4aNu2LXfffTcDBw6MdXUcEpxQb7vdojeEE9YKbN68mWuuuYYdO3aglOKGG27g1ltvrXHMp59+ygUXXED37t0BuOiii7jvvvsiuk5lZSVDhw7l7bffblI/38HBnrHWUKBME/O7QbLkeNu2bRvbtm1j8ODBlJSUUFBQwIwZM+jXr1/wmE8//ZQnn3yyyfPF//3vfzN16tQ6x+gdHCIhnDXQm0vkcetdr48uXbowePBgQOds69u3b6MDYBri3HPPZc+ePYcM3Tk4RIo9RzwWHveEE3koGzZsYPHixQwZMuSQfV9//TXHHXccZ599NitXrmxU+Uqp4JBaPAyFOCQ2LpfrsKmjmmuJ7YQVeWlpKRdffDFPP/002dnZNfYNHjyYjRs3snTpUm655RYuvPDCRl+nT58+nHjiibz++utNrLFDaydWM9YSrk8O2uQ599xzOeuss7j99tsbPL5bt24sWLCg3tlsDbF//35OOeUUZs+efcgDxcEhUmyR13bENTHnOiRLn1xE+MUvfkHfvn3rFfj27duDEWvz5s3DNE06dOjQ6Gu2adOG3/zmNzz++OONLsPBwcblcrXoGmsJN07+5Zdf8tprrwWTSQA88sgjbNq0CdCRcG+//TbPP/88brebtLQ0pkyZ0uT+zvjx4zn55JNZvXq1s3CiQ5MxDINAIBBMBgnN1ydPSHM9Vnz11Vc89NBDvP3224hIs30pDq2D2musNTFTKySLuR4rvvnmG+bOncvy5cvp168fs2bNinWVHBKcps5YC/s6zVZykrFnzx769evHW2+9Rdu2bRkxYkSsq+SQBITOWGsuqzqpRP7BBx/Qu3dv8vPz60z+UFlZyeWXX05+fj5Dhgxhw4YNYZc9evRoLr74YoYOHcpll13G3/72tyjW3KG1UlVVxYoVK/i///s/nn766Wa5RtL0yQOBAMcccwwfffQReXl5FBUV8eabb9YId/3b3/7GsmXLeOGFF5gyZQrTp09n6tSpEV+roqKCoUOH8s4773DEEUdE82M4JCnvvPMOp59+Otu2bWPhwoUsXryYJUuWUFlZSb9+/SgsLOSkk06qM7ArApIjdr0+vv76ayZOnMiHH34IEFye+I9//GPwmLPOOouJEydy4okn4vf7OeKII9i1a1ejHGgzZszgnXfeCc5vd3AIxTRN1q5dy6JFi1i0aBGzZ89mx44djBgxgsLCQk444QQGDx5MmzZtounATe6ppnUldaydnjn0GLfbTZs2bdi9e3ejgmQuuOACnn/+eRYsWFBnTniH1oNpmhQXF7NgwQIWL17MokWL2LVrFz169KCgoIBzzjmH+++/n/vvv5+ioiJ+9rOftWj9kkbkLY1Sij//+c9cf/31fPjhh3GXa9uheRARduzYwcKFC1m0aBGLFy9my5Yt5OXlUVhYyCmnnMLtt99Oly5dDmmhn3rqqZgkeEwakYeT1NE+Ji8vD7/fz/79+5sUCWf3pd58803GjRvX6HIc4hMRYc+ePSxevDjYj163bh05OTkUFhZSWFjIjTfeSNeuXcN6yKekpLRArQ8lafrkfr+fY445hrlz55Kbm0tRURFvvPEG/fv3Dx7z3HPPsXz58qDj7Z133mHatGlNuu6+ffsYPnw4H330EVlZWU39GA4xQkT48MMPmT59On379mXhwoWsXr2a7OxsCgoKKCoqoqioiF69esWz1ZbcjjeAmTNncttttxEIBBg/fjwTJkzgvvvuo7CwkPPPP5+KigquvvpqFi9eTPv27ZkyZQo9evRo8nVfeuklVq1axYMPPhiFT+HQ3IgI5eXlLFu2LNhCf//996SkpLBlyxbGjh3L1VdfTd++fZsagdbSJL/IY0UgEODkk0/mpZdeIj8/P9bVcahFZWUlK1euDAp6+fLlGIbBcccdR0FBASeccALHHnssXq+X4uJinnjiCZ555plYV7sxOCJvLgKBAG+88QaTJk3ilFNO4eGHH060FiBp8Pv9/PDDD8Ghq6VLl+Lz+ejfvz+FhYUUFRUxaNAg0tLSknHuQXIMocXbxJCqqipOOumkYAveqVOnGNcouQl1mAYCAdasWRMU9JIlSygtLaV3794UFRUxduxYnnzySbKysuLqN9PSJExLbtfT/rJ27tyJy+WKyDv++9//nn//+994vV569uzJ5MmTadu27SHHdevWjaysrOCsoAULFoRV/pYtWzj//PP5+OOPo7IgvUM1pmmyadMm3nnnHV566SW6d+/O3r176dmzZ9DkLigooH379q1Z0Mlhrq9YsYJZs2ZRVlZGcXExzz77bNhDE7Nnz+aMM87A7XZz5513AtSZCKIpmWT+9Kc/4fV6ueWWWyI+10EjImzfvp2FCxeycOFClixZwtatW+natSsFBQX88MMP9O7dmwcffLA1C7ouEtNcLy8vZ/v27ezatYtJkyaxbNkyhgwZwoknnshll10W0djjyJEjg//bOdWjzR133BGsW+fOnaNefrIhIuzevTtoci9atIiNGzdyxBFHBFvom2++mby8vODQVVVVVVQSgbQW4rolr6ysDC6KsGXLFvr378+ZZ57JunXr+Oc//8l7772nC21EP/28887j8ssv56qrrjpkX/fu3WnXrh1KKW688UZuuOGGiMr+17/+xfvvv89zzz0X0XnJjohw4MCBYOjnokWLWLNmDe3ataOgoCAY092jR494HouOZxLLXLeFu3TpUnbu3Mnxxx9fw3w+/vjjmTBhApdcckmN80aMGMH27dsPKe/hhx/mggsuCP6/YMEC3nnnnTofDsXFxeTm5rJz507OPPNM/vrXvzJ8+PDwP6QIZ555Jg888ADHH3982OclCwsXLiQvL4/MzEyWLFkSDP/84YcfSE9P5/jjjw8Gl/Tp0weXyxXrKicLiSXyuti4cSPz589n3759fPXVV9xzzz0RB7P87//+Ly+++CJz584lPT29weMnTpxIZmYmd9xxR0TXWbFiBTfddBMffPBBqzArKyoqWLFiBQsXLuS9995jyZIl9OrVi0GDBgWHrgYMGOCsEtu8JKbITdPENE2uvfZafD4fxx9/PH6/n1NOOYXTTjstorI++OADbr/9dj777LN6h7rKysowTZOsrCzKyso488wzue+++xg1alSkVeeWW25h0KBBXHnllRGfG8/4fD6+//77GmPRpmkyYMCAoMn9l7/8hQsvvJBLL7001tVtTSSmyG3++te/MmrUKJYsWUKHDh3o2LFjxCuP5ufnU1lZGRx2Gzp0KC+88AJbt27luuuuY+bMmaxbt+6QddEnTJjQqDrv3buXU089lTlz5pCZmdmoMmJNIBBg1apVNcaiKyoq6Nu3bzCme/DgwWRkZNSwWPbu3UtpaWmN6b8OzU5iitw0zaATZubMmfzwww/06tWLGTNmcMYZZzBu3Li4C5AJ5fnnn2fdunU88MADsa5Kg5imyYYNG4KCXrx4MXv37qVXr15Bk7ugoIC2bdvG7f1u5STmEJot8P3797Ny5UrGjRvHkUceSffu3ZkzZ06Nh0A8csMNN3DSSSexbt26qEyGiQYlJSW88cYbnHvuuTXGonfs2MHRRx9NYWEhI0eO5O6776ZTp06OoJuJxgZdRUrci9xm//79zJ8/n1/96le89NJLzJ49m1tuuSWuBV5RUcH8+fMpKipi1KhR9O/fn+nTp7d4PUSEXbt2BVvohQsX8sUXX/Dmm28yYsQITj75ZG677TaOPPJIR9AtzCeffNLo5bvCJSFELiJ07dqVK664goceeoj09HQmT54c9/O3t27dytSpUyksLGT16tXcdNNNzX5NEWHfvn01xqLXrVtH+/btg4kOxo8fTyAQ4Nprr+Xhhx92hJ3kxH2fvDalpaVBJ1Y0TfWJEyfy8ssvB73ujzzyCKNHjz7kuA8++IBbb72VQCDAddddx1133RVW+Zs2beKiiy5i7ty5URtGEhHKyspqCHrVqlVkZmbWCC7p1atXnWPRe/fupV27dlGpi0PkNDXoqg4S0/HWUoQzHh5O2udwrvGrX/0q4vqJCBUVFSxfvjw4L/q7777D6/XWGIvu37+/M801QWhq0FUdJKbjLZ6YN28e+fn5QQfaFVdcwbvvvhu2yO+8806GDh3KpZdeetgpqSLC73//e6644gqWLVvGokWLWL58OQADBgygqKiIW2+9lYEDB8Ysb1hrIhAIUFhYSG5uLu+//37UyrVzEObk5DBmzBjmzZvXVJHXiSPyEJ599lleffVVCgsLmTRp0iGmbDhpnw9HWloa99xzDw888ADPPvtscLvf72fVqlVBL/fixYvZsGED8+fPZ+zYsYwfP57jjz+e9PR0p/8cA5555hn69u3LgQMHolZm7aCr2bNnB+dpRJv4dU03AyNGjGDAgAGHvN59911uuukm1q5dy5IlS+jSpQu/+93vmqUOl1xyCWvWrOGJJ57grrvu4qyzzuKUU07h8ccfZ9++fVx22WV8+OGHrF27FsMwuOmmmxg2bNghwSYOLcOWLVv4z3/+w3XXXRfVcnfs2MGwYcM47rjjOOGEEzjnnHMaFVUZDq2qJZ8zZ05Yx11//fWce+65h2wPJ+1zQyiluO2225gxYwZjx47lvvvuo0OHDnUK+L///a+TfCLG3HbbbTzxxBOUlJREtdwePXqwdOnSqJZZH62qJT8c27ZtC/4/ffp0BgwYcMgxRUVFrF69mvXr1wfnNJ9//vkRX+uiiy7i1VdfZdSoUXTs2LHeFtoReGx5//33ycnJoaCgINZVaRoi0pKvuOWqq66SAQMGyLHHHivnnXeebN26VUREiouL5eyzzw4e95///Ed69eolPXr0kIceeihW1XWwKC8vl6KiIhk4cKD069dP7rvvvqiVfdddd0lubq4cffTR0rlzZ0lLS5Nx48ZFrfxmoE7dOUNoDgmNWLECmZmZ+Hw+hg0bxjPPPMPQoUOjep1PP/2UJ598Mqre9WagTpPQMdcdEhqlVDA4yufz4fP5HAdlLZyW3CHhCQQCFBQUsGbNGm6++eY6k3O2EpyW3CE2bN68mdNPP51+/frRv3//qK9O4nK5WLJkCVu2bGHevHmsWLEiquUnOk5LHgaXX345P/74I6AXOGzbti1Lliw55LiWmjqYaGzbto1t27YxePBgSkpKKCgoYMaMGWFHCkbCgw8+SHp6esTpupIEJ6y1sUydOjX4/+9+9zvatGlT77EtMXUw0ejSpQtdunQBICsri759+1JcXBwVke/atQuPx0Pbtm0pLy/no48+CubUd9A4Io8AEWHatGl8/PHHsa5KwrJhwwYWL17MkCFDolLetm3buPbaawkEApimyWWXXVZnIFNrxhF5BPz3v/+lc+fO9OrVq879SilGjhwZzamDSUVpaSkXX3wxTz/9NNnZ2VEpc+DAgSxevDgqZSUrjsgtwsnX/uabbx428+oXX3xRY+pgnz59mmVWUXMwfvz4YIRXcziufD4fF198MePGjeOiiy6KevkO9eM43sLE7/eTm5sbXDigIRqbrz1WfP7552RmZnLNNddEXeQiwrXXXkv79u15+umno1q2Qw2cIbSmMGfOHPr06VOvwMvKyoKTGOypg3XFv8crw4cPp3379s1S9pdffslrr73Gxx9/zKBBgxg0aBAzZ85slms5HIpjrofJlClTDjHVQ/O179ix45B87c01dTDRGDZsGC1sMTqE4JjrDkE2bNjAueeem7TBJFIrP//s2bMZP348l1xyCU8//XRc5+8PE8dcT2Q++OADevfuTX5+Po899lisq5NQrFq1in/9618opfD7/cHtBQUF3HrrrXz99dcAiS7wemnpltyhESilXMAq4ExgCzAfuFJEvovydboB74tI4jgT6kAplQPki8hX1vvLgD+KyPHW+2wRORBy/FpgkIhENzNEnOC05InBCcAaEVknIlXAFOCCaF5AKfUm8DXQWym1RSn1i2iW31wopVxKKUPVbIYVcLe1PwOYB/iVUvcopRYCc5RS/ULOKQf6tmjFWxBH5IlBLrA55P0Wa1vUEJErRaSLiHhEJE9E/h7N8htDqHCVpraYEZGAiJgiIkqpNGvzCOBUpdQy4CmgEvAAmUAh8D4wHuhqHf8j+kGalDjedYe4QimVAgwESkTkB3u76H6l1DrWAM63jj8DaKOUugU4ACwDJovIK9axO4F91sPgc+u8fGAjuqU/wTpOSZL1YR2RJwbFQOgawHnWtoTG8jWIiJhKqeeBAvRvsgTYp5SaCUwRkf1KqQHAWUA28H9W18VUSv0KyADOBYYDvwaeBd4CeoZcbg5gxyNvAXzAkdb7L4FLIfgwSSoccz0xmA/0Ukp1V0p5gSuA92Jcp0Zj9aPfBkoBeyraScB7IjJYRE4FngPGAZcrpbKA36Jb8gPA9Uope3H6BegWei/wCfA5cBHwHXB8yGUXo1tugO1AVcj7JUB7pVRSrhnliDwBEBE/uoX6EPgemCYiK2Nbq4ax+tEuy6wOIiIBdD/5bhGxB+U/wGpZlVJpIjIbeBO4EhgFpKJb43zgQuA467wvADtUrxwoQ1sDq7FabqVUrvW+n1V2KbACWKKUSrHeHwASelShPhyRJwgiMlNEjhGRniLycKzrEw5WBtGAiJh17P4WGBTy/jO0uQ1gD2bPBfqjPd8nALcBPwCXishr1jErgIFKqQEi4gNGAl+IyHpgvlLqO+AetIh/HlK3qSIyXUQqlVJ3ovv1SdmSO+PkDs2GUuoY4JfoFnKtiNxkO7aUUqcCj4nIidax7YANItIm1PmllNoHPAx0EZHbQ8rOBXYCJro7U4xu0fcD14nIVqvMUkv8ddXPLSJ+a1x9b33HJTqO482hWVBKpQI3ASvR/oO1UMOx9SOQYQemiMhepVS5UqqP7VVXSl0JfAP8B3hCKfX/0A6zYcB04DkRCSilvgJ2isiDIdc3rH56vR5zqxuEiOw83HGJjmOuOzQXlcBYYA/wrYhsrrV/l7VvUMi2lWgPO0qpUcAlwCtWZN916FiBCmAi8KIVGGSXdax1nscSa7CLEK5wk1Hg4JjrDs1AiEl+P9AJOAJtTk8SkU0h+19Em/FPWOc9DPwRPaRVCrwDvC4i5Q1crxvQSUTmN9+nSlwckTs0O1arfCnwDxH5MmT7L4HhIjLWet8WyBSRLYcpywWYydrqNgdOn9yhWbDGtk9Dh98WovvMX9bq9y5Fj3kfIyKrRGQfsM863wXB4bYgtd+HXC8p+9PRwBG5Q3NhAqPRk0U+tl61+71r0L/B/1NKnWmNV2MdV6eY68MReP045rqDQ5LjeNcdmpW6It7qOSY5MzbEAU5L7uCQ5DgtuYNDkuOI3MEhyXFE7uCQ5Dgid3BIchyROzgkOY7IHRySHEfkDg5Jzv8HdBPAeoqg6jsAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x216 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Trajectories in space-depth\n",
    "plot_2D_space_depth(tot_t_span, trajectory, yn, len(X))"
   ]
  }
 ],
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